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Group Title: Special Series Publication - University of Florida. Agricultural and Biological Engineering Department ; no. SS-AGE-42
Title: Population trends for the United States
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 Material Information
Title: Population trends for the United States nation and states
Series Title: Special series publication (University of Florida. Agricultural and Biological Engineering Dept.)
Physical Description: 12, 52 leaves : ill. ; 28 cm.
Language: English
Creator: Overman, Allen R., 1937-
Pirozzoli, Heather J
Thourot, Charles S
University of Florida -- Agricultural and Biological Engineering Dept
Publisher: Agricultural and Biological Engineering Dept., University of Florida
Place of Publication: Gainesville
Publication Date: 1996]
 Subjects
Subject: Population -- Statistics -- United States   ( lcsh )
Population -- History -- Statistics -- United States   ( lcsh )
Genre: federal government publication   ( marcgt )
bibliography   ( marcgt )
statistics   ( marcgt )
non-fiction   ( marcgt )
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Bibliography: Includes bibliographical references (leaf 8).
Statement of Responsibility: by Allen R. Overman, Heather J. Pirozzoli and Charles S. Thourot.
General Note: "September 1996."
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Table of Contents
    Front Cover
        Front cover 1
    Abstract
        Page 1
    Main
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Full Text





















Agricultural and Biological Engineering Department
Special Series Publication SS-AGE-42


September 1996


Population Trends for the United States


Nation and States







by


Allen R. Overman, Heather J. Pirozzoli and Charles S. Thourot









POPULATION TRENDS FOR THE UNITED STATES


NATION AND STATES


Allen R. Overman, Heather J. Pirozzoli and Charles S. Thourot


ABSTRACT

This document summarizes population trends in the United States for the
200-year period between 1790 and 1990. The first official Census was taken in
1790 after adoption of the constitution in 1789. Population increased steadily from
3,929,000 in 1790 to 248,710,000 in 1990. In 1990 the net rate of growth was
approximately 2,300,000 persons/year. If the early geometric trend of 1790 through
1850 had continued, then U. S. population would have reached approximately 1
billion by the year 1980. Analysis of the past trend for the period 1850 through
1990 by the logistic model, on the other hand, projects a maximum population of
461 million. States exhibit a variety of patterns. Advanced phase of growth is
characterized by reaching more than 75% of projected maximum by the 1990
Census, which includes 14 states. Rapid phase reached less than 50% of
projected maximum, which includes 13 states. Undetermined includes those states
for which the growth trends are not clear, which includes 15 states. The remaining
8 states are between rapid and advanced phases of growth. According to the
logistic model, U.S. population is projected to reach 307 million (75% of maximum)
around the year 2036. Rapid population growth will generate large demands for
agricultural production, engineering services, education, and information. Our
challenge in the academic community is to provide training and information to meet
these needs. The format of this document gives a numerical and graphical portrait
of the nation and of each state, and is intended to provide information to the public
and professionals alike. Literature references are given for persons interested in
further reading on this subject.



Allen R. Overman, Heather J. Pirozzoli and Charles S. Thourot are Professor,
Staff Assistant, and Graduate Research Assistant, respectively, Agricultural &
Biological Engineering Department, UF/ IFAS, University of Florida, Gainesville, FL
32611-0570.







Population Trends for the United States Overman, Pirozzoli & Thourot, 1996


POPULATION TRENDS FOR THE UNITED STATES: NATION AND STATES

INTRODUCTION

An informed public on key issues is important for future planning. Population
growth affects each of us and everything we do. This document provides
information on the population trends in the nation and states in a form not readily
available elsewhere. Census data are presented in both tabular and graphical
format, so the reader can view the results and draw individual conclusions. Where
trends are clear enough to do so, a model has been fitted to data and projections
made into the near future. Outside the range of data used to calibrate the models,
projections are shown as dashed curves and lines to call attention to the
uncertainty of estimates.
A wide range of views has been expressed on the subject of population.
Growth drives rising demand for agricultural production, engineering services,
education, and information. More than a quarter century ago Paul Ehrlich at
Stanford University called attention to the runaway growth of the world population
(Ehrlich, 1968) and to the serious implications in store. This message was updated
in 1990 (Ehrlich and Ehrlich, 1990). The demands on the natural system and
stress on the environment have been pointed out by Lester Brown of the
Worldwatch Institute (Brown, 1995; Brown and Kane, 1994) and Joel Cohen of
Rockefeller University (Cohen, 1995). Contrasting views of Norman Meyers
(environmentalist) and Julian Simon (economist) have been published (Myers and
Simon, 1994). It is easy to become confused about this subject, and to tune out
the entire discussion. A very readable book on geography and related topics
(including population) is that of Harm de Blij (de Blij, 1995).
Analysis of population trends involves two aspects: (1) data and (2) models.
Various sources (Cohen, 1995, Appendix 2) have summarized estimates of world
population. Data for the United States are taken from the Census conducted every
decade. The database for the states is taken from Kurian (1994), and can also be
found in the World Almanac published each year and is readily available in most
communities. Models cover a wide spectrum from the geometric model of Malthus
to the logistic model of Verhulst to more complicated demographic models which
incorporate geographic and age distributions (Caswell, 1989). We have chosen
the logistic model because it describes the essence of the trends and is relatively
easy to use. It has been used to model various social indicators (Marchetti, 1986).
Application of the logistic model to forage production has been discussed by
Overman (1995). Virtually all models are open to criticism at some level. The
viewpoint of Charles Babbage (Mackay, 1991) appears relevant to our case: Errors
using inadequate data are much less than those using no data at all.
This document follows the same format as the companion document on state
and county population trends for Florida (Overman et al., 1996).







Population Trends for the United States Overman, Pirozzoli & Thourot, 1996

MODELS

This document focuses on two models of population: (1) geometric and (2)
logistic. Both are relatively simple mathematically and are useful in describing
general trends. Benjamin Franklin pointed out in 1755 that the U.S. population
appeared to double every 25 years. In 1798 Thomas Malthus published an essay
on population (Petersen, 1979) in which he noted the tendency toward geometric
(exponential) increase:

Population, when unchecked, increases in a geometric ratio.
Subsistence only increases in an arithmetic ratio.

The essay set off a debate which continues to this day. Since such a trend can not
continue indefinitely due to a number of factors (such as availability of resources,
accumulation of wastes, maintenance of essential functions), the Belgian
mathematician Verhulst proposed the logistic sigmoidd) model, which is
self-limiting in structure. These models have the forms

geometric: P = Po ek (Y 1800) [1]

logistic: P = A / [1 + eb c (Y -1800)] [2]

where

P = estimated population
Y = year
Po = estimated population at year 1800
k = geometric response coefficient
A = estimated maximum population
b = logistic intercept parameter
c = logistic response coefficient

Both models can be rewritten in linearized form to describe straight lines on
semilog paper:

geometric: In [P/Po] = k (Y 1800) [3]

logistic: In [P/(A P)] = c (Y 1800) b [4]

The logistic model is considered to be the more realistic of the two, since it
approaches a maximum and is self-limiting. We use this model to estimate trends
and projections (where feasable) for the states. A minimum of 6 data points
(50-year span) are used to calibrate the model. Trends were inadequate to
perform regression analysis for 15 states.







Population Trends for the United States Overman, Pirozzoli & Thourot, 1996

NATIONAL TREND

The U. S. trend is best illustrated by the log graph shown in Figure 1. Note that
the vertical axis is logarithmic, and covers the range 3.93 million (3,929,000) in
1790 to 249 million (248,710,000) in 1990. The straight line is given by

P (millions) = 5.32 e0.0294 (Y -1800) [5]

for data from 1790 through 1850. Several things may be noted. The geometric
(Malthus) model describes the trend rather well for this period, with an average
doubling time of 24 years. If this trend had continued, then the U.S. population
would have reached 1 billion by the year 1980. It is clear from Figure 1 that the
relative (logarithmic) rate of growth slowed down considerably after 1850. In our
view, a more realistic alternative is to use the logistic model to describe the U.S.
trend from 1850 onward. The maximum value A = 461 million for Eq. [2] can be
obtained by nonlinear regresssion. Data can then be reduced to the form shown in
Figure 2, where the line is given by

In [P/(A P)] = 0.0204 (Y 1800) 3.72 [6]

It follows that the logistic model for the national trend becomes

P (millions) = 461 / [1 + e3.72 0.0204 (Y 1800)] [7]

Results can be presented in linear graphical form shown in Figure 3, where the
curve is drawn from Eq. [7]. Parameters listed in Eqs. [6] and [7] (viz. 461, 3.72,
and 0.0204) represent best estimates by statistical procedures. This model
projects a population of 230 million (50% of maximum) by the year 1982 and 307
million (75% of maximum) by 2036. The linearized plot helps to identify trends
which are described by the logistic model and is used in the analysis of state data.
The geometric and logistic models both show a stronger persistence in
population growth than is often perceived. Expectation that this trend will abruptly
level off appears rather unrealistic. What seems more likely is that the rate of
growth will eventually slow down and population approach some maximum value,
as has occurred in England & Wales (see Figure 4).
It has been pointed out that no simple model appears adequate for long-term
projections (Cohen, 1995, p. 96).







Population Trends for the United States Overman, Pirozzoli & Thourot, 1996

STATE TRENDS

In the remainder of this report we adopt a one-page format to show trends for
each state in the United States. This format includes Census data, graphs showing
data along with estimates and projections (where appropriate), model parameters,
and equations. For this purpose we use only the logistic model, referenced to the
year 1800. Parameter estimates by nonlinear regression include maximum
population (A), intercept parameter (b), and response coefficient (c). Note that
Yo.5o and Yo.75 are years when population is estimated to reach 50% and 75%,
respectively, of projected maximum. Linear and log graphs cover the period 1800
until 2050. The straight line portion of the log graphs lends support to the utility of
the logistic model. Dashed curves and lines have been used beyond 1990 to
emphasize uncertainty of the projections. Model parameters for the states are
summarized in Table 1, except where trends were inadequate to make estimates
by the logistic model.
Growth patterns can be characterized in a variety of ways, of which we choose
the following classification. Advanced phase of growth is characterized by having
reached more than 75% of projected maximum by the 1990 Census. Rapid phase
describes those which have reached less than 50% of projected maximum.
Undetermined include those states for which data are insufficient to evaluate the
model. The remaining 8 states are between rapid and advanced phases of growth.

EXAMPLE

Alabama data are used for a detailed description of results. The population
grew from approximately 1,000 in 1800 to 4,041,000 in 1990 as shown in the linear
graph. It is apparent from the log graph that the logistic model describes the trend
during the period 1850-1990. Statistical analysis of data during this time interval
gives the parameters listed in the table, so that the model becomes

P (millions) = 5.0 / [1 + e2.78 0.0220(Y 1800)] [8]

To make estimates from Eq. [8] a calculator which contains the function ex is
-0.51
needed. Substitution of Y = 1950 into Eq. [8] leads to e = 0.600 and gives
the estimate P = 3,112,000 for 1950, compared to the census value of 3,062,000,
an error of 1.6%. Similarly, the estimate for 1990 is 3,987,000, compared to
4,041,000 for an error of 1.4%. These estimates confirm the accuracy of the
parameters. Projections can be made by choosing a future time. For example, for
the year 2020 the projected population would be 4,412,000, or 89% of estimated
maximum. It should be emphasized again that these are projections and are not to
be taken as absolute. Many factors, such as public policy and events in the rest of
the world, may cause actual values to come out either lower or higher than
projected.







Population Trends for the United States Overman, Pirozzoli & Thourot, 1996

Table 1. Parameters for Logistic Trends in the United States.


Unit A b c Y.50 Y075 Ref.

millions yr-1


United States 461 3.72 0.0204 1982 2036 1800

Alabama 5.0 2.78 0.0220 1927 1977 1800
Alaska 2.1 8.28 0.0380 2018 2047 1800
Arizona 11.1 9.23 0.0449 2006 2030 1800
Arkansas -
California 45.5 7.75 0.0440 1975 2000 1800
Colorado 6.3 6.48 0.0347 1986 2018 1800
Conneticut 5.4 3.91 0.0233 1968 2015 1800
Delaware -
Florida 44.2 8.87 0.0421 2011 2037 1800
Georgia 32.4 4.15 0.0141 2093 2170 1800
Hawaii 2.5 5.48 0.0275 1999 2039 1800
Idaho -
Illinois 12.5 3.87 0.0330 1917 1951 1800
Indiana -
Iowa -
Kansas -
Kentucky 4.3 2.12 0.0197 1908 1964 1800
Louisiana 7.9 3.63 0.0202 1980 2034 1800
Maine 5.4 2.53 0.0063 2200 2375 1800
Maryland 5.6 7.81 0.0503 1955 1977 1800
Massachusetts 6.6 3.18 0.0284 1912 1951 1800
Michigan 11.9 4.60 0.0322 1943 1977 1800
Minnesota 4.5 4.20 0.0345 1922 1953 1800
Mississippi 2.6 2.69 0.0303 1889 1925 1800
Missouri 6.6 2.48 0.0196 1927 1983 1800
Montana -
Nebraska -
Nevada 2.8 12.15 0.0624 1995 2012 1800
New Hampshire -
New Jersey 10.0 4.48 0.0305 1947 1983 1800
New Mexico 3.5 5.50 0.0276 1999 2039 1800
New York 21.1 3.34 0.0282 1918 1957 1800
North Carolina 17.3 3.82 0.0175 2018 2081 1800
North Dakota -







Population Trends for the United States Overman, Pirozzoli & Thourot, 1996


Table 1. (continued).


Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming


16.0

4.6
12.7
1.1
16.7

17.8
79.6
9.5

10.6
7.9

5.6


3.12

5.47
3.18
3.41
3.82

3.42
5.56
6.06

5.00
5.70

3.49


0.0213

0.0315
0.0323
0.0297
0.0129

0.0129
0.0223
0.0238

0.0279
0.0323

0.0276


1947 1998


1973
1898
1915
2097

2065
2049
2054


2008
1932
1952
2182

2150
2099
2100


1979 2019
1977 2011


1926


1966


No analysis was performed for states with dashed (-) entries due to insufficient
trends.

SUMMARY

Results of this document are relevant to agriculture, engineering, education,
and the public in general. Large challenges are ahead for resource management
and environmental quality.
This document does not advocate any public policy or reaction to these trends.
Some will view these trends favorably, while others will see them in a negative
context. This is a complex issue with implications at county, state, national, and
international levels. Information is provided here to enlighten public discussion and
debate.


1800

1800
1800
1800
1800

1800
1800
1800

1800
1800

1800







Population Trends for the United States Overman, Pirozzoli & Thourot, 1996


REFERENCES

Brown, L. R. 1995. Who Will Feed China? W. W. Norton & Co. New York, NY.

Brown, L. R. and H. Kane. 1994. Full House. W. W. Norton & Co. New York, NY.

Caswell, H. 1989. Matrix Population Models. Sinauer Associates, Inc.
Sunderland, MA.

Cohen, J. E. 1995. How Many People Can the Earth Support? W. W. Norton &
Co. New York, NY.

de Blij, H. 1995. Geography Book. John Wiley & Sons. New York, NY.

Ehrlich, P. R. 1968. The Population Bomb. Ballantine. New York, NY.

Ehrlich, P. R. and A. H. Ehrlich. 1990. The Population Explosion. Simon and
Schuster. New York, NY.

Kurian, G. T. 1994. Datapedia of the United States 1790-2000. Bernan Press.
Lanham, MD.

Mackay, A. L. 1991. A Dictionary of Scientific Quotations. Institute of Physics
Publishing. Philadelphia, PA.

Marchetti, C. 1986. Stable Rules in Social Behavior. IBM Conference. Brazilian
Academy of Sciences. Brasilia, Brazil.

Marth, D. and M. J. Marth. 1990. Florida Almanac 1990-1991. Pelican
Publishing Co. Gretna, FL.

Myers, N. and J. L. Simon. 1994. Scarcity or Abundance? A Debate on the
Environment. W. W. Norton & Co. New York, NY.

Overman, A. R. 1995. Rational Basis for the Logistic Model for Forage Grasses.
J. Plant Nutrition 18:995-1012.

Overman, A. R., H. J. Pirozzoli and C. S. Thourot. 1996. Population Trends for
Florida: State and Counties. Special Series Publication SS-AGE-41.
University of Florida. Gainesville, FL.

Petersen, W. 1979. Malthus. Harvard University Press. Cambridge, MA.






Population Trends for the United States


1000


1800 1850 1900 1950 2000


2050


Year
Figure 1. United States Population Trend Log Scale.


I I I I I
Exponential

United States / Logistic


/


Z-




I I I I I


100


10


1


1750


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


10 2




0 1


100


10^ -
10-2

e 0
0
10-2 )-IIII

1800 1850 1900 1950 2000 2050

Year

Figure 2. United States Population Trend Linearized Plot.


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States Overman, Pirozzoli & Thourot, 1996


450

400

350

300

250

200

150

100

50

1800
1800


1950 2000 2050


Figure 3. United States Population Trend Linear Scale.


1850 1900

Year








Population Trends for the United States Overman, Pirozzoli & Thourot, 1996


60







c 40
0


0
o 2

E

o

a. 20


0 I I I I I I I
1750 1800 1850 1900 1950 2000 2050 2100

Year

Figure 4. England & Wales Population Trend Linear Scale.


I I I I I I


England and Wales


-







Population Trends for the United States


United States


Year Population
1790 3,929,000
1800 5,308,000
1810 7,240,000
1820 9,638,000
1830 12,861,000
1840 17,063,000
1850 23,192,000
1860 31,443,000
1870 38,558,000
1880 50,189,000
1890 62,980,000
1900 76,212,000
1910 92,228,000
1920 106,022,000
1930 123,203,000
1940 132,165,000
1950 151,326,000
1960 179,323,000
1970 203,302,000
1980 226,542,000
1990 248,710,000


Parameter Estimates
A 461,000,000
b 3.72
c 0.0204
Yo.5o 1982
Yo.75 2036


A
P b-c(Y- )
1 + eb-c(Y-1800)


450 I I I I
400 -
United States
350 -
o 300 -
E250 -
0
S200
g 150
100 -
50

1800 1850 1900 1950 2000 2050

Year
Linear plot of population


10.2 V
1800


1850 1900 1950


2000 2050


Year
Log plot of population


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.50 = year for 50% maximum
Y0.5 = year for 75% maximum


Notes:

10-1 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


Overman, Pirozzoli & Thourot, 1996


In(A P) = c(Y- 1800)-b







Population Trends for the United States


Alabama


Year Population
1790 --
1800 1,000
1810 9,000
1820 128,000
1830 310,000
1840 591,000
1850 772,000
1860 964,000
1870 997,000
1880 1,263,000
1890 1,513,000
1900 1,829,000
1910 2,138,000
1920 2,348,000
1930 2,646,000
1940 2,833,000
1950 3,062,000
1960 3,267,000
1970 3,444,000
1980 3,890,000
1990 4,041,000


Parameter Estimates
A 4,980,000
b 2.79
c 0.0220
Yo.so 1927
Yo.75 1977


1 + eb-c(Y-1800)


SIn p =c(Y-1800)-b
[(A P)]


P = population estimate
Y = year


A
b =
c =
Yo.50
Yo.75


estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


g0o I I I1 I
1800 1850 1900 1950 2000

Year
Linear plot of population


10-2 I I
1800 1850 1900 1950


2000


Year
Log plot of population


Notes:

10-1 = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


I I I I


Alabama


2050


2050


I I I I


A = 4,980,000


-
-o


Overman, Pirozzoli & Thourot, 1996






Population Trends for the United States


Alaska


Year Population
1790
1800
1810
1820
1830
1840
1850
1860
1870 --
1880 33,000
1890 32,000
1900 64,000
1910 64,000
1920 55,000
1930 59,000
1940 73,000
1950 129,000
1960 226,000
1970 300,000
1980 400,000
1990 550,000


Parameter Estimates
A 2,140,000
b 8.28
c 0.0380
Yo.5o 2018
Yo.75 2047


0.0 1
1800


A
P=
1 + eb-c(Y-1800)


10-2 L
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000 2050


Year
Log plot of population


P = population estimate
Y = year
A = estimated maximum population


b =
c =
Yo.50
Y0.75


intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


Notes:


101 = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
----------= projection


Overman, Pirozzoli & Thourot, 1996


ln[(A P) c(Y-1800)- b
[(A P)]J







Population Trends for the United States


Arizona


Year Population
1790
1800
1810
1820
1830
1840
1850
1860 --
1870 10,000
1880 40,000
1890 88,000
1900 123,000
1910 204,000
1920 334,000
1930 436,000
1940 499,000
1950 750,000
1960 1,302,000
1970 1,771,000
1980 2,718,000
1990 3,665,000


Parameter Estimates
A 11,100,000
b 9.23
c 0.0449
Yo.so 2006
Yo.75 2030


1 + ebc(Y
1+ eb-c(Y-1800)


2 -


0 -
1800


10-2 L
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000 2050


In (Ap = c(Y-1800)- b
[(A -P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo0., = year for 50% maximum
Y0.75 = year for 75% maximum


Year
Log plot of population


Notes:

101 = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
----------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Arkansas


Year Population
1790 --
1800
1810 1,000
1820 14,000
1830 30,000
1840 98,000
1850 210,000
1860 435,000
1870 484,000
1880 803,000
1890 1,128,000
1900 1,312,000
1910 1,574,000
1920 1,752,000
1930 1,854,000
1940 1,949,000
1950 1,910,000
1960 1,786,000
1970 1,923,000
1980 2,286,000
1990 2,351,000


Parameter Estimates
A --
b --
c --
Yo.50
o.75 --


A
P=
1+ eb-c(Y-1800)

In -p- = c(Y -1800)-b
[(A P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo0.o = year for 50% maximum
Yo.5 = year for 75% maximum


2.5

2.0

1.5

1.0

0.5

f rt


UV.VU
1800


1850 1900


1950 2000 2050


Year
Linear plot of population


Notes:

no apparent logistic trend


I I I I

Arkansas

0 0
0
0


0
00
0
^ oI I I I


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


California


Year Population
1790 --
1800
1810
1820
1830
1840 --
1850 93,000
1860 380,000
1870 560,000
1880 865,000
1890 1,213,000
1900 1,485,000
1910 2,378,000
1920 3,427,000
1930 5,677,000
1940 6,907,000
1950 10,586,000
1960 15,717,000
1970 19,953,000
1980 23,668,000
1990 29,760,000


Parameter Estimates
A 45,500,000
b 7.75
c 0.0440
Yo.5o 1975
Yo.75 2000


0
1800


A
P=
1 + eb-c(Y-1800)


10-2
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000 2050


In P = c(Y 1800)- b
[(A -P)


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
YO.50 = year for 50% maximum
Y0.75 = year for 75% maximum


Year
Log plot of population


Notes:

10-1 = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Colorado


Year Population
1790
1800
1810
1820
1830
1840
1850 --
1860 34,000
1870 40,000
1880 194,000
1890 413,000
1900 540,000
1910 799,000
1920 940,000
1930 1,036,000
1940 1,123,000
1950 1,325,000
1960 1,754,000
1970 2,207,000
1980 2,890,000
1990 3,294,000


Parameter Estimates
A 6,270,000
b 6.48
c 0.0307
Yo.5o 1986
Yo.75 2018


A
P + ec(Y )
1 + e b-c(Y-1800)


5


/
Colorado /
/
/


3

2 -


0 l
1800


1850 1900
1850 1900


1 I
1950 2000 2050


Year
Linear plot of population


10-2 .
1800


I I

A = 6,270,000







00,0(



I/ i


1850 1900 1950


I I




/
/


I I


2000 2050


In = c(Y-1800)-b
(A P)


P = population estimate
Y = year


A=
b =
c =
Yo.50
Y0.75


estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


Year
Log plot of population


Notes:

10' = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Connecticut


Year Population
1790 238,000
1800 251,000
1810 262,000
1820 275,000
1830 298,000
1840 310,000
1850 371,000
1860 460,000
1870 537,000
1880 623,000
1890 746,000
1900 908,000
1910 1,115,000
1920 1,381,000
1930 1,607,000
1940 1,709,000
1950 2,007,000
1960 2,535,000
1970 3,032,000
1980 3,108,000
1990 3,287,000


Parameter Estimates
A 5,430,000
b 3.91
c 0.0233
YO.sO 1967
Yo.75 2015


0 0-
1800


A
P= c
1 + eb-c(Y-1800)


10-2 L
1800


ln P ]= (Y-1800)-b


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
YO.0 = year for 50% maximum
Yo.75 = year for 75% maximum


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950
Year


2000 2050


Log plot of population


Notes:

101 = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Delaware


Year Population
1790 59,000
1800 64,000
1810 73,000
1820 73,000
1830 77,000
1840 78,000
1850 92,000
1860 112,000
1870 125,000
1880 147,000
1890 168,000
1900 185,000
1910 202,000
1920 223,000
1930 238,000
1940 267,000
1950 318,000
1960 446,000
1970 548,000
1980 594,000
1990 666,000


Parameter Estimates
A --
b --
c --
Yo.50
Y.75 --


A
P=
1 + eb-c(Y-1800)

(AI P = c(Y-1800)-b


P = population estimate
Y = year
A = estimated maximum population


b =
c =
Yo.50
Yo.75


intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


0.8


U)
o 0.6
E

S 0.4
Cc

0L


I.


1800 1850 1900 1950
1800 1850 1900 1950


I I I 1

S Delaware

0
0
0
0

0
- o 000
0000
I I I
O


2000 2050


Year
Linear plot of population


Notes:

no apparent logistic trend


Overman, Pirozzoli & Thourot, 1996


0 0







Population Trends for the United States


Florida


Year Population
1790
1800
1810
1820 --
1830 35,000
1840 54,000
1850 87,000
1860 140,000
1870 188,000
1880 269,000
1890 391,000
1900 529,000
1910 753,000
1920 968,000
1930 1,468,000
1940 1,897,000
1950 2,771,000
1960 4,952,000
1970 6,789,000
1980 9,746,000
1990 12,938,000


Parameter Estimates
A 44,200,000
b 8.87
c 0.0421
Yo.so 2011
Y0.75 2037


1 + eb-cY-
1 + eb-c(Y-1800)


5
1800
1800


102
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


n[ (AP ](Y-1800)-b
[(A P)]


population estimate
year
estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


Year
Log plot of population


Notes:

10" = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
----------= projection


2000 2050


P
Y =
A=
b =
c =
Yoso
Y0.50
Y0.75


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Georgia


Year Population
1790 83,000
1800 163,000
1810 252,000
1820 341,000
1830 517,000
1840 691,000
1850 906,000
1860 1,057,000
1870 1,184,000
1880 1,542,000
1890 1,837,000
1900 2,216,000
1910 2,609,000
1920 2,896,000
1930 2,909,000
1940 3,124,000
1950 3,445,000
1960 3,943,000
1970 4,590,000
1980 5,463,000
1990 6,478,000


Parameter Estimates
A 32,400,000
b 4.15
c 0.0141
YO.s0 2093
Y0.75 2172


1800 1850 1900 1950 2000 2050


Year
Linear plot of population


100


10-1


~ 2


A
P=
1 + e b-c(Y-1800)


-1! -


1800 1850 1900 1950 2000 2050


In (AP = c(Y-1800)-b
[(A P)


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y.50 = year for 50% maximum
Yo.75 = year for 75% maximum


Year
Log plot of population


Notes:

101 = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
----------= projection


I I I I

A = 32,400,000










SI*0
O I I I I


Overman, Pirozzoli & Thourot, 1996


,v







Population Trends for the United States


Hawaii


Year Population
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890 --
1900 154,000
1910 192,000
1920 256,000
1930 368,000
1940 423,000
1950 500,000
1960 633,000
1970 769,000
1980 965,000
1990 1,108,000


Parameter Estimates
A 2,550,000
b 5.48
c 0.0275
YO.s0 1999
Y0.75 2039


0.5 -


0.0 -
1800


101


A
P 1 + eb
1 + eb-c(Y-1800)


10-2 1
1800


I P) = c(Y- 1800)-b



P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.5o = year for 50% maximum
Y0.75 = year for 75% maximum


1850 1900 1950 2000 2050

Year
Linear plot of population


I I I I

A = 2,550,000










/
de
.0 I I I
1850 1900 1950 2000 2050


Year
Log plot of population


Notes:

10-1 = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
----------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Idaho


1.4

1.2

1.0
0
- 0.8
E
o 0.6

. 0.4
0
a-


Year Population
1790
1800
1810
1820
1830
1840
1850
1860 --
1870 15,000
1880 33,000
1890 89,000
1900 162,000
1910 326,000
1920 432,000
1930 445,000
1940 525,000
1950 589,000
1960 667,000
1970 713,000
1980 944,000
1990 1,007,000


Parameter Estimates
A -
b --
c --
Y0.50
Y0.75 --


A
P=
1 + eb-c(Y-1800)


In PA c(Y -1800)-b


p =
Y =
A =
b =
c =
Yoso
Y0.50
Y0.75


population estimate
year
estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


I-


0.2 -

0.0
1800


I I I

Idaho
0
0

0
0
0
00
0

0
O0
I no I I I


1850 1900 1950 2000

Year
Linear plot of population


Notes:

no apparent logistic trend


2050


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Illinois


Year Population
1790
1800 --
1810 12,000
1820 55,000
1830 157,000
1840 476,000
1850 851,000
1860 1,712,000
1870 2,540,000
1880 3,078,000
1890 3,826,000
1900 4,822,000
1910 5,639,000
1920 6,485,000
1930 7,631,000
1940 7,897,000
1950 8,712,000
1960 10,081,000
1970 11,114,000
1980 11,427,000
1990 11,431,000


Parameter Estimates
A 12,500,000
b 3.87
c 0.0330
Yo.50 1917
Yo.75 1951


P= b-c(Y )
I eb-c(Y-1800)


2

0 L
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


/
/ 0


10-2 1 0
1800 11


/
A = 12,500,000







0


850


1900 1950


2000


2050


Year
Log plot of population


In c (Y 1800)-b
[(A P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.50 = year for 50% maximum
Yo.7s = year for 75% maximum


Notes:


10" = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
---------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Indiana


Year Population
1790 --
1800 6,000
1810 25,000
1820 147,000
1830 343,000
1840 686,000
1850 988,000
1860 1,350,000
1870 1,681,000
1880 1,978,000
1890 2,192,000
1900 2,516,000
1910 2,701,000
1920 2,930,000
1930 3,239,000
1940 3,428,000
1950 3,934,000
1960 4,662,000
1970 5,194,000
1980 5,490,000
1990 5,544,000


Parameter Estimates
A --
b --
c
C --
Yo.50
Yo.75 --


A
P=
1+ eb-c(Y-1800)

In P = c(Y 1800) b
.(A-P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.5o = year for 50% maximum


6
Indiana 00

0
4 0



2 O
0
0
0
1 0
0
Al 1_ __ I I II


1800 1850 1900 1950


2000 2050


Year
Linear plot of population


Notes:

no apparent logistic trend


= year for 75% maximum


Overman, Pirozzoli & Thourot, 1996


Yo.75







Population Trends for the United States


Iowa


Year Population
1790
1800
1810
1820
1830 --
1840 43,000
1850 192,000
1860 675,000
1870 1,194,000
1880 1,625,000
1890 1,912,000
1900 2,232,000
1910 2,225,000
1920 2,404,000
1930 2,471,000
1940 2,538,000
1950 2,621,000
1960 2,758,000
1970 2,824,000
1980 2,914,000
1990 2,777,000


Parameter Estimates
A --
b --
c --
Y0.50
Y0.75 --


A
1 + eb-c(Y-1800)

In[ ( = c(Y-1800)-b


0)
' 2.0
E

g 1.5-
. 1.0
0
0.5


0.0 I-
1800


P = population estimate
Y = year
A = estimated maximum population


b =
c =
Yo.50
Y0.75


1850 1900 1950 2000 2050

Year
Linear plot of population


Notes:

no apparent logistic trend


intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


Iowa 00 0
0000
00
0
0

0

0

0


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Kansas


Year Population
1790 --
1800
1810
1820
1830
1840
1850 --
1860 107,000
1870 364,000
1880 996,000
1890 1,428,000
1900 1,470,000
1910 1,691,000
1920 1,769,000
1930 1,881,000
1940 1,801,000
1950 1,905,000
1960 2,179,000
1970 2,247,000
1980 2,364,000
1990 2,478,000


Parameter Estimates
A --
b --
c --
Y0.50
YO.75 --


A
P=
1+ eb-c(Y-1800)

In p) = c(Y 1800)-b


P
Y =
A=
b =
c =
Y0.50
Y0.75


2.5

2.0

1.5

1.0


0.0 I-
1800


population estimate
year
estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


1850 1900 1950 2000

Year
Linear plot of population


Notes:

no apparent logistic trend


I I I I

Kansas 00
o
00


00

0


0
10 I I I


2050


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Kentucky


Year Population
1790 74,000
1800 221,000
1810 407,000
1820 564,000
1830 688,000
1840 780,000
1850 982,000
1860 1,156,000
1870 1,321,000
1880 1,649,000
1890 1,859,000
1900 2,147,000
1910 2,290,000
1920 2,417,000
1930 2,615,000
1940 2,846,000
1950 2,945,000
1960 3,038,000
1970 3,219,000
1980 3,661,000
1990 3,685,000


Parameter Estimates
A 4,340,000
b 2.12
c 0.0917
Yo.50 1908
Yo.7s 1964


A
P +
1 + eb-c(Y-1800)


1800 1850 1900 1950 2000 2050

Year
Linear plot of population


10-2
1800


1850 1900 1950


2000 2050


In p = c(Y-1800)-b
L(A -P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.s, = year for 50% maximum
Yo.7s = year for 75% maximum


Year
Log plot of population


Notes:

10'1 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


I I I I


A = 4,340,000


I I I


Overman, Pirozzoli & Thourot, 1996


I







Population Trends for the United States


Louisiana


Year Population
1790
1800 --
1810 77,000
1820 153,000
1830 216,000
1840 352,000
1850 518,000
1860 708,000
1870 727,000
1880 940,000
1890 1,119,000
1900 1,382,000
1910 1,656,000
1920 1,799,000
1930 2,102,000
1940 2,364,000
1950 2,684,000
1960 3,257,000
1970 3,641,000
1980 4,206,000
1990 4,220,000


Parameter Estimates
A 7,940,000
b 3.63
c 0.0202
Y.50 1980
Y0.75 2034


1 + eb-c(Y-1800)


In -P-\= c(Y-O1800)-b
(A P)J


P = population estimate
Y = year
A = estimated maximum population


b =
c =
Yo.5o
Yo.75


intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


0 -.%o I I I I
1800 1850 1900 1950 2000 2050

Year
Linear plot of population


A = 7,940,000
101 -


100


10- -

0
10-2 I I I
1800 1850 1900 1950 2000 2050
Year
Log plot of population


Notes:

101' = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
---------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Maine


Year Population
1790 97,000
1800 152,000
1810 229,000
1820 298,000
1830 399,000
1840 502,000
1850 583,000
1860 628,000
1870 627,000
1880 649,000
1890 661,000
1900 694,000
1910 742,000
1920 768,000
1930 797,000
1940 847,000
1950 914,000
1960 969,000
1970 992,000
1980 1,125,000
1990 1,228,000


Parameter Estimates
A 5,450,000
b 2.53
c 0.0063
Yo.so 2200
Yo.75 2375


1.5 "


1.0


0.U
1800


A
P
1 + eb-c(Y-1800)


10-2 L
1800


1850 1900 1950 2000

Year
Linear plot of population


1850 1900 1950


2050


In ] = c(Y-1800)-b
[(A P) ]


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.0 = year for 50% maximum
Yo.75 = year for 75% maximum


Year
Log plot of population


Notes:

10' = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
----------= projection


Maine
-f
/
0 t





1
.e
I II


2000 2050


I I I I


Overman, Pirozzoli & Thourot, 1996


n rI







Population Trends for the United States


Maryland


Year Population
1790 320,000
1800 342,000
1810 381,000
1820 407,000
1830 447,000
1840 470,000
1850 583,000
1860 687,000
1870 781,000
1880 935,000
1890 1,042,000
1900 1,188,000
1910 1,295,000
1920 1,450,000
1930 1,632,000
1940 1,821,000
1950 2,343,000
1960 3,101,000
1970 3,922,000
1980 4,217,000
1990 4,781,000


Parameter Estimates
A 5,580,000
b 7.81
c 0.503
Yo.5o 1955
Yo.75 1977


A
P=
1+e b-c(Y-1800)


0 -
1800


1850 1900 1950 2000 2050


Year
Linear plot of population


10-2
1800


1850 1900 1950


n (A = (Y-1800)-b
[(A P) J


P = population estimate
Y = year
A = estimat'er maximuim 1rr1l- t


Year
Log plot of population


Notes:


popua on 10 = 10% of maxnnu


i 1 n-i rn, f


2000 2050


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Massachusetts


Year Population
1790 379,000
1800 423,000
1810 472,000
1820 523,000
1830 610,000
1840 738,000
1850 995,000
1860 1,231,000
1870 1,457,000
1880 1,783,000
1890 2,239,000
1900 2,805,000
1910 3,366,000
1920 3,852,000
1930 4,250,000
1940 4,317,000
1950 4,691,000
1960 5,149,000
1970 5,689,000
1980 5,737,000
1990 6,016,000


Parameter Estimates
A 6,580,000
b 3.18
c 0.0284
Yo.50 1912
Yo.75 1951


0 L-
1800


1n-2


1 + c(Y )
1 + eb-c(Y-1800)


1850 1900 1950 2000 2050

Year
Linear plot of population


1800 1850 1900 1950


2000


2050


In -P = c(Y -1800)-b
[(A P)]


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.5 = year for 50% maximum
Yo., = year for 75% maximum


Year
Log plot of population


Notes:

10"1 = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
---------= projection


I I I I

A = 6,580,000


I I I I


Overman, Pirozzoli & Thourot, 1996


I V






Population Trends for the United States


Michigan


Year Population
1790
1800 --
1810 5,000
1820 9,000
1830 32,000
1840 212,000
1850 398,000
1860 749,000
1870 1,184,000
1880 1,637,000
1890 2,094,000
1900 2,421,000
1910 2,810,000
1920 3,668,000
1930 4,842,000
1940 5,256,000
1950 6,372,000
1960 7,823,000
1970 8,875,000
1980 9,262,000
1990 9,295,000


Parameter Estimates
A 11,900,000
b 4.60
c 0.0322
Yo.5o 1943
Yo.75 1977


1 + eb-c(Y-1800)


21

0 0
1800


10-2 /.
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000 2050


n (A = (Y- 1800)- b
[(A P)]


population estimate
year
estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


Year
Log plot of population


Notes:

10" = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


p =
Y =
A=
b =
c =
Yo.5o
Yo.75


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Minnesota


Year Population
1790 --
1800
1810
1820
1830
1840 --
1850 6,000
1860 172,000
1870 440,000
1880 781,000
1890 1,310,000
1900 1,751,000
1910 2,076,000
1920 2,387,000
1930 2,564,000
1940 2,792,000
1950 2,982,000
1960 3,414,000
1970 3,805,000
1980 4,076,000
1990 4,375,000


Parameter Estimates
A 4,540,000
b 4.20
c 0.0345
Yo0.0 1922
Yo.75 1953


1 b-c(Y )
1 + e b-c(Y-1800)


In P = c(Y-1800)-b
[(A P)


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y0.50 = year for 50% maximum
Y0.75 = year for 75% maximum


00- 185
1800 1850


1900 1950 2000


2050


Year
Linear plot of population


10-2 I I I
1800 1850 1900 1950


2000


2050


Year
Log plot of population


Notes:

10" = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


I I I I


Minnesota


4 -


I I I


A =4,540,000 I I
A = 4,540,000 O


/ 0


,


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Mississippi


Year Population
1790 --
1800 8,000
1810 31,000
1820 75,000
1830 137,000
1840 376,000
1850 607,000
1860 791,000
1870 828,000
1880 1,132,000
1890 1,290,000
1900 1,551,000
1910 1,797,000
1920 1,791,000
1930 2,010,000
1940 2,184,000
1950 2,179,000
1960 2,178,000
1970 2,217,000
1980 2,521,000
1990 2,573,000


Parameter Estimates
A 2,570,000
b 2.69
c 0.0303
Y0.s0 1889
YO.75 1925


1 + eb-c(Y-1800)


n (AP) c(Y-1800)- b
[(A P)j


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.0 = year for 50% maximum
Y0.7 = year for 75% maximum


2.51-


1.5 -

1.0 -

0.5 -


1800 1850


1900 1950 2000 2050


Year
Linear plot of population


10-1
0
e
10-2 10 I
1800 1850 1900 1950


2000


2050


Year
Log plot of population


Notes:

10" = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


I I I I


uU-


I I1 I

A = 2,570,000 /


II li ..


-.


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Missouri


Year Population
1790 --
1800 --
1810 20,000
1820 67,000
1830 140,000
1840 384,000
1850 682,000
1860 1,182,000
1870 1,721,000
1880 2,168,000
1890 2,679,000
1900 3,107,000
1910 3,293,000
1920 3,404,000
1930 3,629,000
1940 3,785,000
1950 3,995,000
1960 4,320,000
1970 4,677,000
1980 4,917,000
1990 5,117,000


Parameter Estimates
A 6,620,000
b 2.48
c 0.0196
YO.so 1927
Yo.75 1983


A
P=1+
1 + b-c(Y-1800)


1


1800 U--1850
1800 1850 1900


1950 2000


Year
Linear plot of population


10-2 L0 I I I
1800 1850 1900 1950


2000


InP = i=c(Y-1800)-bpA
[(A P) e

P = population estimate


Y =
A=
b =
c =
Yo.50
\I


year
estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
.. _- l 2 t"fy/ .. -" ..... .


0.75 year for /79/o maximum


Year
Log plot of population


Notes:


10" = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression


I I I I

Missouri




- ooo,


/
/0


I I
A e"


2050


A = 6,620,000




eo

^60
0


2050





Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Montana

Year Population 1.0 I I
1790
1800 -- 0.8 Montana o0
1810
1820 0- 0
1830 -- 0.6 -
1840 E
1850 0.4
1860 --
1870 21,000 0 0
1880 39,000 0.2
1890 143,000 0
1900 243,000 0.0 00 1
1910 376,000 1800 1850 1900 1950 2000 2050
1920 549,000
1930 538,000 Year
1940 559,000 Linear plot of population


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Overman, Pirozzoli & Thourot, 1996


Nebraska


2.0



1.5

C
.2
E 1.0

C
o
0o

o 0.5
a-


-


0.0 L
1800


i I I i

Nebraska 00

0
00





0
0

I 0 I I I


1850 1900 1950


2000 2050


Year
Linear plot of population


Parameter Estimates
A --
b --
c --
Y0.50
Y0.75 --


A
P=
1 eb-c(Y-1800)


[ P = c(Y-1800)-b
[(A P)


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y0.50 = year for 50% maximum
Yo.75 = year for 75% maximum


Notes:

no apparent logistic trend










Population Trends for the United States


Nevada


Year Population
1790 --
1800
1810
1820
1830
1840
1850 --
1860 7,000
1870 42,000
1880 62,000
1890 47,000
1900 42,000
1910 82,000
1920 77,000
1930 91,000
1940 110,000
1950 160,000
1960 285,000
1970 489,000
1980 800,000
1990 1,202,000


Parameter Estimates
A 2,820,000
b 12.2
c 0.0624
YO.s0 1995
Yo.75 2012


0.5 -


0.0 -
1800


A
P= c
1+ eb-c(Y-1800)


10-2 I
1800


In [P = c(Y-1800)-b
n(A P)


P = population estimate
Y = year
A = estimated maximum population


b =
c =
Y0.50
Yo.75


intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000


2050


Year
Log plot of population


Notes:

10' = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


A = 2,820,000
/
/
/
/


0 000
p 0I O /


Overman, Pirozzoli & Thourot, 1996


I I







Population Trends for the United States


New Hampshire


1.4

1.2

1.0
C
o
S0.8
E
0.6

E 0.4
0
a-


Year Population
1790 142,000
1800 184,000
1810 214,000
1820 244,000
1830 269,000
1840 285,000
1850 318,000
1860 326,000
1870 318,000
1880 347,000
1890 377,000
1900 412,000
1910 431,000
1920 443,000
1930 465,000
1940 492,000
1950 533,000
1960 607,000
1970 738,000
1980 921,000
1990 1,109,000


Parameter Estimates
A --
b --
c --
Yo.50
Yo.75 --


A
P=
1 + eb-c(Y-1800)


I(n P = c(Y-1800)-b


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.0 = year for 50% maximum
Yo.75 = year for 75% maximum


U.0
1800


1850 1900 1950 2000

Year
Linear plot of population


Notes:

no apparent logistic trend


New Hampshire 0

0

0
0

--
- 00000000
I I I


I I II


2050


Overman, Pirozzoli & Thourot, 1996


nr






Population Trends for the United States


New Jersey


Year Population
1790 184,000
1800 211,000
1810 246,000
1820 278,000
1830 321,000
1840 373,000
1850 490,000
1860 672,000
1870 906,000
1880 1,131,000
1890 1,445,000
1900 1,884,000
1910 2,537,000
1920 3,156,000
1930 4,041,000
1940 4,160,000
1950 4,835,000
1960 6,067,000
1970 7,168,000
1980 7,365,000
1990 7,730,000


Parameter Estimates
A 10,000,000
b 4.48
c 0.0308
Yo.50 1947
Yo.,5 1983


1 + eb-c(Y-1800)


1800 1850 1900 1950 2000 2050


Year
Linear plot of population


101


10-2 k
1800


In (A =c(Y-1800)-b
[(A P)


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y0.0 = year for 50% maximum
Y.75 = year for 75% maximum


I 1

A= 10,000,000


I I


1850 1900 1950


2000


2050


Year
Log plot of population


Notes:

10"' = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


New Mexico


Year Population
1790
1800
1810
1820
1830
1840 --
1850 62,000
1860 94,000
1870 92,000
1880 120,000
1890 160,000
1900 195,000
1910 327,000
1920 360,000
1930 423,000
1940 532,000
1950 681,000
1960 951,000
1970 1,016,000
1980 1,303,000
1990 1,515,000


Parameter Estimates
A 3,480,000
b 5.50
c 0.0276
Y0.50 1999
Yo.75 2039


P= +
1 + eb-c(Y-1800)


2.5

. 2.0
E
d 1.5 -
0 .
0o 1.0 -

0.5

0.0 -
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


10-2 1 / 1
1800 1850 1900


1950


2000


2050


In = c(Y- 1800)-b
[(A -P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo., = year for 50% maximum
Y.75 = year for 75% maximum


Year
Log plot of population


Notes:

10" = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
----------= projection


1 I I I

A =3,480,000


/
- ~


I I


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


New York


Year Population
1790 340,000
1800 589,000
1810 959,000
1820 1,373,000
1830 1,919,000
1840 2,429,000
1850 3,097,000
1860 3,881,000
1870 4,383,000
1880 5,083,000
1890 6,003,000
1900 7,269,000
1910 9,114,000
1920 10,385,000
1930 12,588,000
1940 13,479,000
1950 14,830,000
1960 16,782,000
1970 18,237,000
1980 17,558,000
1990 17,990,000


Parameter Estimates
A 21,100,000
b 3.34
c 0.0282
YO.s0 1918
Yo.75 1957


1 + eb-c(Y-1800)


1800 1850 1900 1950 2000 2050


Year
Linear plot of population


10-2
18C


ln[ (A (Y-1800)-b
[(A P)


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y0.50 = year for 50% maximum
Y7,5 = year for 75% maximum


1850 1900 1950


2000


2050


Year
Log plot of population


Notes:

10'" = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


I I I

A =21,100,000 -
4-


I I


I


Overman, Pirozzoli & Thourot, 1996


)0






Population Trends for the United States


North Carolina


Year Population
1790 394,000
1800 478,000
1810 556,000
1820 639,000
1830 738,000
1840 753,000
1850 869,000
1860 993,000
1870 1,071,000
1880 1,400,000
1890 1,618,000
1900 1,894,000
1910 2,206,000
1920 2,559,000
1930 3,170,000
1940 3,572,000
1950 4,062,000
1960 4,556,000
1970 5,082,000
1980 5,882,000
1990 6,629,000


Parameter Estimates
A 17,300,000
b 3.82
c 0.0175
YO.s0 2018
Yo.75 2081


2

1800
1800


A
P=
1 + eb-c(Y-1800)


10-2 L
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000 2050


In P = c(Y-1800)-b
[(A P)]


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo0.s = year for 50% maximum
Yo.75 = year for 75% maximum


Year
Log plot of population


Notes:

10"' = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
----------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


North Dakota


Year Population
1790
1800
1810
1820
1830
1840
1850 --
1860 5,000
1870 2,000
1880 37,000
1890 191,000
1900 319,000
1910 577,000
1920 647,000
1930 681,000
1940 642,000
1950 620,000
1960 632,000
1970 618,000
1980 653,000
1990 639,000


Parameter Estimates
A --
b --
c --
Yo.50
Yo0.75 --


A
P=
1 + eb-c(Y-1800)

I" ( p) c(Y-1800)-b


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.0 = year for 50% maximum
Yo.75 = year for 75% maximum


0.8


0.6


0.4


0.2


0.0
1800


1850 1900 1950 2000

Year
Linear plot of population


Notes:

no apparent logistic trend


I I I I

North Dakota


0



0


I I I


2050


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Oklahoma


Year Population
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880 --
1890 259,000
1900 790,000
1910 1,657,000
1920 2,028,000
1930 2,396,000
1940 2,336,000
1950 2,233,000
1960 2,328,000
1970 2,559,000
1980 3,025,000
1990 3,146,000


Parameter Estimates
A --
b --
c --
Yo.50
Yo.75 --


A
P=
1 + eb-c(Y-1800)

In P- cP(Y-1800)-b
[(A P)


P =
Y =
A=
b =
c =
Yo.5o
Yo.75


population estimate
year
estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


3.0

2.5

2.0

1.5

1.0

0.5

0.0
18C


1850 1900 1950


2000 2050


Year
Linear plot of population


Notes:

no apparent logistic trend


0
Oklahoma
0
OQO
00


0


0
0

I I I I


Overman, Pirozzoli & Thourot, 1996


)0







Population Trends for the United States


Ohio


Year Population
1790 --
1800 45,000
1810 231,000
1820 581,000
1830 938,000
1840 1,519,000
1850 1,980,000
1860 2,340,000
1870 2,665,000
1880 3,198,000
1890 3,672,000
1900 4,158,000
1910 4,767,000
1920 5,759,000
1930 6,647,000
1940 6,908,000
.1950 7,947,000
1960 9,706,000
1970 10,652,000
1980 10,798,000
1990 10,847,000


Parameter Estimates
A 16,000,000
b 3.12
c 0.0213
Yo.5o 1947
Yo.75 1998


A
P=
1 + eb-c(Y-1800)


10 1-


1800 1850 1900 1950 2000

Year
Linear plot of population


lU -
1 00

10-2 18 I
1800 1850


1900 1950


In p = c(Y-1800)-b
[(A P)]


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo0., = year for 50/o maximum
Yo.7 = year for 75% maximum


Year
Log plot of population


Notes:

101 = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


Ohio


n A6' I I I I


2050


2050


I I I I


A = 16,000,000


I I


2000


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States

Oregon


Year Population
1790 --
1800
1810
1820
1830
1840 --
1850 12,000
1860 52,000
1870 91,000
1880 175,000
1890 318,000
1900 414,000
1910 673,000
1920 783,000
1930 954,000
1940 1,090,000
1950 1,521,000
1960 1,769,000
1970 2,091,000
1980 2,633,000
1990 2,842,000


Parameter Estimates
A 4,570,000
b 5.47
c 0.0315
YO.50 1973
Yo.75 2008


Overman, Pirozzoli & Thourot, 1996


0 L
1800


A
P1 =
1 + eb-c(Y-1800)


In p- = c(Y-1800)-b
[(A P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.5o = year for 50% maximum
Yo.75 = year for 75% maximum


10-2 l
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000


2050


Year

Log plot of population


Notes:

101 = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


I I I4,

A = 4,570,000


/ in I I I







Population Trends for the United States


Pennsylvania


Year Population
1790 434,000
1800 602,000
1810 810,000
1820 1,049,000
1830 1,348,000
1840 1,724,000
1850 2,312,000
1860 2,906,000
1870 3,522,000
1880 4,283,000
1890 5,258,000
1900 6,302,000
1910 7,665,000
1920 8,720,000
1930 9,631,000
1940 9,900,000
1950 10,498,000
1960 11,319,000
1970 11,794,000
1980 11,864,000
1990 11,882,000


Parameter Estimates
A 12,700,000
b 3.18
c 0.0323
Yo.5o 1898
Yo.75 1932


1 + b-c(Y )
I+ eb-c(Y-1800)


21

0
1800


101


1850 1900 1950 2000 2050

Year
Linear plot of population


10-2 I 1
1800 1850


1900 1950


2000


2050


n (P = c(Y-1800)-b
[(A P)]


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y0.50 = year for 50% maximum
Yo.75 = year for 75% maximum


Year
Log plot of population


Notes:

10"1 = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


S 1 I

A = 12,700,000 /


| | |


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Rhode Island


Year Population
1790 69,000
1800 69,000
1810 77,000
1820 83,000
1830 97,000
1840 109,000
1850 148,000
1860 175,000
1870 217,000
1880 277,000
1890 346,000
1900 429,000
1910 543,000
1920 604,000
1930 687,000
1940 713,000
1950 792,000
1960 859,000
1970 947,000
1980 947,000
1990 1,003,000


Parameter Estimates
A 1,100,000
b 3.41
c 0.0297
Yo.50 1915
Yo.75 1952


1 + eb-c(Y-1800)


0.2

0.0
1800


10-2 1
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000 2050


In P = c(Y-1800)-b
[(A -P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.0o = year for 50% maximum
Y0.7s = year for 75% maximum


Year
Log plot of population


Notes:

10' = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
---------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


South Carolina


Year Population
1790 249,000
1800 346,000
1810 415,000
1820 503,000
1830 581,000
1840 594,000
1850 669,000
1860 704,000
1870 706,000
1880 996,000
1890 1,151,000
1900 1,340,000
1910 1,515,000
1920 1,684,000
1930 1,739,000
1940 1,900,000
1950 2,117,000
1960 2,383,000
1970 2,591,000
1980 3,122,000
1990 3,487,000


Parameter Estimates
A 16,700,000
b 3.82
c 0.0129
Yo.5o 2097
Yo.7s 2182


0 L
1800


A
P c(Y
1 + eb-c(Y-1800)


In P = c(Y- 1800)- b
[(A P)]


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo0. = year for 50%o maximum
Y0.75 = year for 75% maximum


1850 1900 1950 2000 2050

Year
Linear plot of population


A = 16,700,000
101 -


100


10-1 0-


10-2 I I I
1800 1850 1900 1950 2000 2050
Year
Log plot of population


Notes:

10' = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Overman, Pirozzoli & Thourot, 1996


South Dakota


Year Population
1790
1800
1810
1820
1830
1840
1850
1860 --
1870 12,000
1880 98,000
1890 349,000
1900 402,000
1910 584,000
1920 637,000
1930 693,000
1940 643,000
1950 653,000
1960 681,000
1970 666,000
1980 691,000
1990 696,000


Parameter Estimates
A --
b --
c --
Yo.50
Yo.75 --


A
P=
1+ eb-c(Y-1800)

n = c(Y-1800)-b
[(A P)]


P = population estimate
Y = year
A = estimated maximum
b = intercept parameter
c = response coefficient
Yo0. = year for 50% maxi
Yo.75 = year for 75% maxi


0.8 F


r
o 0.6
E
e-
. 0.4
a
o
Q- n i


F


Al I


u.u
1800


I I I I

South Dakota

000000
0

0
0



0


I tie I I|


1850 1900


1950 2000 2050


Year
Linear plot of population


Notes:


Spopi


imum
imum


nation


no apparent logistic trend







Population Trends for the United States


Texas


Year Population
1790 --
1800
1810
1820
1830
1840 --
1850 213,000
1860 604,000
1870 819,000
1880 1,592,000
1890 2,236,000
1900 3,049,000
1910 3,897,000
1920 4,663,000
1930 5,825,000
1940 6,415,000
1950 7,711,000
1960 9,580,000
1970 11,197,000
1980 14,229,000
1990 16,987,000


Parameter Estimates
A 79,900,000
b 5.56
c 0.0223
YO.50 2049
Yo.5 2099


10 -


180
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1 + eb-c(Y-1800)


10-2
1800


1850 1900 1950


2000 2050


In- P = c(Y-1800)- b
[(A P).


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y0.5 = year for 50% maximum
Yo75 = year for 75% maximum


Year
Log plot of population


Notes:


10- = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Utah


Year Population
1790
1800
1810
1820
1830
1840 --
1850 11,000
1860 40,000
1870 87,000
1880 144,000
1890 211,000
1900 277,000
1910 373,000
1920 449,000
1930 508,000
1940 550,000
1950 689,000
1960 891,000
1970 1,059,000
1980 1,461,000
1990 1,723,000


Parameter Estimates
A 9,570,000
b 6.06
c 0.0238
Yo.5o 2054
Yo.7s 2100


0 -
1800


A
P=
1 + eb-c(Y-1800)


10-2
180


ln[(A = c(Y-1800)- b
[(A P)


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y0.0 = year for 50%ol maximum
Yo.7s = year for 75% maximum


10


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950 2000


2050


Year
Log plot of population


Notes:

101 = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------= projection


I I I I

A = 9,570,000


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Vermont


Year Population
1790 85,000
1800 154,000
1810 218,000
1820 236,000
1830 281,000
1840 292,000
1850 314,000
1860 315,000
1870 331,000
1880 332,000
1890 332,000
1900 344,000
1910 356,000
1920 352,000
1930 360,000
1940 359,000
1950 378,000
1960 390,000
1970 444,000
1980 511,000
1990 563,000


Parameter Estimates
A --
b --
c --
Yo.50
1Y.75 --


A
P=
1 + eb-c(Y-1800)

In[ = c(Y-1800)-b


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Y.50 = year for 50% maximum
Yo.75 = year for 75% maximum


0.8 I


U,
. 0.6
E
. 0.4
-i
0
QL n n


)


0.0 L


I I I I

Vermont



0
0
0
-O



00o00000000000
.>0


I I I I


1800 1850


1900 1950


2000 2050


Year
Linear plot of population


Notes:

no apparent logistic trend


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


Virginia


Year Population
1790 692,000
1800 808,000
1810 878,000
1820 938,000
1830 1,044,000
1840 1,025,000
1850 1,119,000
1860 1,220,000
1870 1,225,000
1880 1,513,000
1890 1,656,000
1900 1,854,000
1910 2,062,000
1920 2,309,000
1930 2,422,000
1940 2,678,000
1950 3,319,000
1960 3,967,000
1970 4,648,000
1980 5,347,000
1990 6,187,000


Parameter Estimates
A 10,600,000
b 5.00
c 0.0279
Yo.so 1979
Yo.7s 2019


A
P1
1 + eb-c(Y-1800)


2


1
18(


1850 1900 1950


2000 2050


Year
Linear plot of population


10-2 L1
1800


1850 1900 1950


In P) c(Y- 1800)-b
S(A -P)J


P = population estimate
Y = year
A = estimated maximum population


b =
c =
Y0.50
Yo.75


intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


Year
Log plot of population


Notes:

10" = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
----------= projection


I I I I

S Virginia

/ /

/




000oo00
,0000000 ./
-- r


2000 2050


I I |


Overman, Pirozzoli & Thourot, 1996


8


30







Population Trends for the United States

Tennessee


Overman, Pirozzoli & Thourot, 1996


Year Population
1790 36,000
1800 106,000
1810 262,000
1820 423,000
1830 682,000
1840 829,000
1850 1,003,000
1860 1,110,000
1870 1,259,000
1880 1,542,000
1890 1,768,000
1900 2,021,000
1910 2,185,000
1920 2,338,000
1930 2,617,000
1940 2,916,000
1950 3,292,000
1960 3,567,000
1970 3,924,000
1980 4,591,000
1990 4,877,000


Parameter Estimates
A 17,800,000
b 3.42
c 0.0129
Y0.s0 2065
Yo.75 2150


A
P1 +
1 + eb-c(Y-1800)


p =
Y =
A=
b =
c =
Yo.5o
Yo.75


1800 1850 1900 1950 2000 2050


Year


Linear plot of population


S -2 I-
iu *


population estimate
year
estimated maximum population
intercept parameter
response coefficient
= year for 500/ maximum
= year for 75% maximum


|U ---- --- ---- -- -- ----
1800 1850 1900 1950 2000 20
Year
Log plot of population


Notes:

101 = 10% of maximum population
100 = 50% of maximum population
10' = 90% of maximum population
= regression
--------- projection


50


I I I I

A = 17,800,000








- ^

0 I I I I


I


In (A = c(Yl-1800)-b







Population Trends for the United States


Washington


Year Population
1790
1800
1810
1820
1830
1840 --
1850 1,000
1860 12,000
1870 24,000
1880 75,000
1890 357,000
1900 518,000
1910 1,142,000
1920 1,357,000
1930 1,563,000
1940 1,736,000
1950 2,379,000
1960 2,853,000
1970 3,409,000
1980 4,132,000
1990 4,867,000


Parameter Estimates
A 7,860,000
b 5.70
c 0.0323
YO.s0 1977
Yo.75 2011


1 + b-c(Y
1 + e b-c(Y-1800)


0 L
1800


10-2
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000 2050


In (AP)=c(Y-1800)-b
[(A P)] =


P = population estimate
Y = year
A = estimated maximum population


b =
c =
Yo.50
Yo.75


intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


Year
Log plot of population


Notes:


10- = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression
--------= projection


Overman, Pirozzoli & Thourot, 1996







Population Trends for the United States


West Virginia


Year Population
1790 56,000
1800 79,000
1810 105,000
1820 137,000
1830 177,000
1840 225,000
1850 302,000
1860 377,000
1870 442,000
1880 618,000
1890 763,000
1900 959,000
1910 1,221,000
1920 1,464,000
1930 1,729,000
1940 1,902,000
.1950 2,006,000
1960 1,860,000
1970 1,744,000
1980 1,950,000
1990 1,793,000


Parameter Estimates
A --
b --
c --
Y0.50
Y0.75


A
P=
1 + eb-c(Y-1800)

In[P = c(Y-1800)-b
[(A P)


P
Y =
A =
b =
c =
C --

Yo.5so
Y0.7S


population estimate
year
estimated maximum population
intercept parameter
response coefficient
= year for 50% maximum
= year for 75% maximum


.0- I I I I

2.0 West Virginia 0
0 00
C
S1.5 o
E 0
. 1.0 0
. 0
o o
S0.5 0


0.0 00
1800 1850 1900 1950 2000 2(


050


Year
Linear plot of population


Notes:

no apparent logistic trend


Overman, Pirozzoli & Thourot, 1996






Population Trends for the United States

Wisconsin


Year Population
1790
1800
1810
1820
1830 --
1840 31,000
1850 305,000
1860 776,000
1870 1,055,000
1880 1,315,000
1890 1,693,000
1900 2,069,000
1910 2,334,000
1920 2,632,000
1930 2,939,000
1940 3,138,000
1950 3,435,000
1960 3,952,000
1970 4,418,000
1980 4,706,000
1990 4,892,000


Parameter Estimates
A 5,650,000
b 3.49
c 0.0276
YO.s0 1926
Yo.75 1966


Overman, Pirozzoli & Thourot, 1996


0 '
1800


A
P= c
1+ eb-c(Y-1800)


10-2 1
1800


1850 1900 1950 2000 2050

Year
Linear plot of population


1850 1900 1950


2000 2050


n P = c(Y-1800)-b
[(A -P)J


P = population estimate
Y = year
A = estimated maximum population
b = intercept parameter
c = response coefficient
Yo.50 = year for 50% maximum


Year
Log plot of population


Notes:

10'1 = 10% of maximum population
100 = 50% of maximum population
101 = 90% of maximum population
= regression




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