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Consider the following. Year 1790 1800 1810 1820 P(t) = 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 143.56 1+35.53e(-0.0353-1) 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.) Year 1820 1910 12.866 17.069 23.192 31.433 38.558 (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. 50.156 62.948 75.996 91.972 Census Population. (in Millions) 9.638 91.972 105.711 122.775 131.669 150.697 Predicted Population (in Millions, rounded to three decimal places) 9.989 9.174 X Error (rounded to three decimal places) -0.351 0 % Error (rounded to two decimal places) -3.64 0 ✓ % %

Consider the following. Year 1790 1800 1810 1820 P(t) = 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 143.56 1+35.53e(-0.0353-1) 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.) Year 1820 1910 12.866 17.069 23.192 31.433 38.558 (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. 50.156 62.948 75.996 91.972 Census Population. (in Millions) 9.638 91.972 105.711 122.775 131.669 150.697 Predicted Population (in Millions, rounded to three decimal places) 9.989 9.174 X Error (rounded to three decimal places) -0.351 0 % Error (rounded to two decimal places) -3.64 0 ✓ % %

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Consider the following. Year 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 P(t) = (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.) 143.56 1+ 35.53e Year Population (in millions) 3.929 5.308 7.240 9.638 12.866 17.069 23.192 31.433 38.558 50.156 62.948 75.996 91.972 1820 (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. 1910 -0.0353-t) 105.711 122.775 131.669 150.697 Census Population (in Millions) 9.638 91.972 Predicted Population (in Millions, rounded to three decimal places) 9.989 9.174 X Error (rounded to three decimal places) -0.351 0 % Error (rounded to two decimal places) -3.64 0 % %
Transcribed Image Text:Consider the following. Year 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 P(t) = (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.) 143.56 1+ 35.53e Year Population (in millions) 3.929 5.308 7.240 9.638 12.866 17.069 23.192 31.433 38.558 50.156 62.948 75.996 91.972 1820 (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. 1910 -0.0353-t) 105.711 122.775 131.669 150.697 Census Population (in Millions) 9.638 91.972 Predicted Population (in Millions, rounded to three decimal places) 9.989 9.174 X Error (rounded to three decimal places) -0.351 0 % Error (rounded to two decimal places) -3.64 0 % %
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