Consider the following. Year 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 Year 1810 1890 Population (in millions) 3.929 5.308 7.240 9.638 (a) Census data for the United States between 1790 and 1950 are given in the table above. Construct a logistic population model using the data from 1790, 1860, and 1920. (Assume that this years since 1790 and P is population in millions. Round all coefficients to four decimal places.) P(t) = Census Population (in Millions) 7.24 12.866 17.069 23.192 (b) Construct a table comparing actual census population with the population predicted by the model in part (a). Compute the error and the percentage error for each entry pair. 62.948 31.433 38.558 50.156 62.948 75.996 91.972 105.711 122.775 131.669 150.697 Predicted Population (in Millions, rounded to three decimal places) Error (rounded to three decimal % Error (rounded to two decimal places) places) % %
Consider the following. Year 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 Year 1810 1890 Population (in millions) 3.929 5.308 7.240 9.638 (a) Census data for the United States between 1790 and 1950 are given in the table above. Construct a logistic population model using the data from 1790, 1860, and 1920. (Assume that this years since 1790 and P is population in millions. Round all coefficients to four decimal places.) P(t) = Census Population (in Millions) 7.24 12.866 17.069 23.192 (b) Construct a table comparing actual census population with the population predicted by the model in part (a). Compute the error and the percentage error for each entry pair. 62.948 31.433 38.558 50.156 62.948 75.996 91.972 105.711 122.775 131.669 150.697 Predicted Population (in Millions, rounded to three decimal places) Error (rounded to three decimal % Error (rounded to two decimal places) places) % %
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Differential Equation
Transcribed Image Text:Consider the following.
Year
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
Year
1810
Population (in millions)
3.929
5.308
7.240
9.638
(a) Census data for the United States between 1790 and 1950 are given in the table above. Construct a logistic population model using the
data from 1790, 1860, and 1920. (Assume that t is years since 1790 and P is population in millions. Round all coefficients to four decimal
places.)
P(t) =
1890
(b) Construct a table comparing actual census population with the population predicted by the model in part (a). Compute the error and the
percentage error for each entry pair.
12.866
17.069
23.192
Census
Population
(in Millions)
7.24
62.948
31.433
38.558
50.156
62.948
75.996
91.972
105.711
122.775
131.669
150.697
Predicted Population
(in Millions, rounded to three
decimal places)
Error (rounded to three decimal % Error (rounded to two decimal
places)
places)
%
%
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