(a). Read the article Food, Land, Population, and the American Economy from Carrying Capacity Network.
(b). Use the historic census data from the U.S. Census Bureau at www.census.gov for the United States for the years 1790 to present to find an exponential model of the form P = a ∙ bt, where t is the number of years after 1790. To do this, first take the logarithm of P. Now find the least-squares regression line between log P and t. The least-squares model is of the form log P = log a + t log b. To find estimates of a and b, compute 10log a, where log a is the intercept and 10log b is the slope of the least-squares regression line. The quantity b - 1 is the growth rate as a decimal. For example, if b = 1.01, then the annual growth rate is 1.01 - 1 = 0.01 or 1%.
(c). Multiply your model obtained in part 2 by 1.2 to obtain a function for the number of arable acres of land A required to have a diverse diet in the United States (as a function of time).
(d). Determine the number of acres of farmland A in the United States for the most recent 9 years for which data are available. Find the least-squares regression line treating year as the explanatory variable.
(e). Determine when the United States will no longer be capable of providing a diverse diet for its entire population by setting the model in part 3 equal to the model in part 4 and solving for the year t.
(f). Does this result seem reasonable? Discuss some reasons why this prediction might be affected or changed. For example, rather than looking at the number of arable acres of land required to have a diverse diet, consider total food production. Compare the results using this variable as a measure of subsistence.