In 1798. Thomas Malthus published An Essay on the Principle of Population in which he stated Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will show the immensity of the first power in comparison of the second What did he mean by this? Essentially he is claiming that population grows exponentially and food production increases linearly. The assumption is that the population grows unchecked-that is, without interference from human-caused or natural disasters such as war, famine, disease, and so on. Malthus also stated (c) Multiply your model obtained in part (b) by 1.2 to fland By that law of our nature which makes food necessary to the life of man, the effects of these two unequal powers must be kept equal. Thi implies a strong and constantly operating check on population from the difficulty of subsistence. Thi difficulty must fall somewhere and must necessarily be severely felt by a large portion of mankind. required to have a diverse diet in the United States (as a function of time). [Hint: The model is A 1.2P.] (d) Go to the Statistical Abstract of the United States and look up 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 ar 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 (c) equal to the model in part (d) and solving for the year (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. (a) Read the article Food, Land, Population, and the American Economy from Carrying Capacity Network rces (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-b, where r 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 t log b. To find estimates of a and b s the s the intercept and 10 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 1.01-1-001 or 1%