Using the U.S. census data in Table 3.1 for 1900, 1920, and 1940 to determine parameters in the logistic equation model, what populations does the model predict for
Using the U.S. census data in Table 3.1 for 1900, 1920, and 1940 to determine parameters in the logistic equation model, what populations does the model predict for
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Using the U.S. census data in Table 3.1 for 1900, 1920, and 1940 to determine parameters in the logistic equation model, what populations does the model predict for 2000 and 2010? Compare your answers with the census data for those years.

Transcribed Image Text:### Comparison of Malthusian and Logistic Models with U.S. Census Data
The following table details a comparative study of the Malthusian and Logistic models in relation to the U.S. Census data for population growth over the years. The population values are given in millions.
| Year | U.S. Census Population (in millions) | Malthusian Model Population (Example 3) | Logistic Model Population (Example 4) | \(\frac{1}{p}\frac{dp}{dt}\) | Logistic (Least Squares) |
|------|--------------------------------------|-----------------------------------------|---------------------------------------|-----------------------------|--------------------------|
| 1790 | 3.93 | 3.93 | 3.03 | | 4.11 |
| 1800 | 5.31 | 5.14 | 5.30 | 0.0312 | 5.42 |
| 1810 | 7.24 | 6.84 | 7.13 | 0.0299 | 7.14 |
| 1820 | 9.63 | 9.13 | 9.58 | 0.0292 | 9.30 |
| 1830 | 12.87 | 11.72 | 12.82 | 0.0289 | 12.33 |
| 1840 | 17.07 | 15.73 | 17.07 | 0.0302 | 16.14 |
| 1850 | 23.19 | 20.76 | 22.80 | 0.0310 | 21.05 |
| 1860 | 31.44 | 27.40 | 29.70 | 0.0285 | 27.33 |
| 1870 | 38.26 | 36.18 | 38.86 | 0.0235 | 35.28 |
| 1880 | 50.19 | 47.72 | 49.71 | 0.0231 | 45.21 |
| 1890 | 62.98 | 62.
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