2. The population of Canada [1] was 24,070,000 in 1980, while in 1990 it was 26,620,000. The population in Kenya [1] was 16,681,000 in 1980, while it was 24,229,000 in 1990.

a. Over a limited range of years, the population P_n of most countries can be estimated using the Malthusian growth law, which is given by:

where n is the number of years since 1980 with P₀ the population in 1980. Find the general solution for this equation, writing an expression for the population P_n for each of these countries with the appropriate values of both P₀ and r from the data given to you. What does the value of r represent? (Don't forget that the data are at 1980 and 1990, while n is in years.)

b. Find how long it takes for each of their populations to double.

c. Find when the population of Canada is equal to the population of Kenya. Graph the populations of both countries between 1980 and 2030.

d. Assuming the populations continue to grow according to the Malthusian growth law above, then determine the populations of these countries in the years 2000, 2050, and 2100. Create a table showing these values.

[1] Statistical Abstract of the U. S., 1995, The National Data Book, 115th ed., U. S. Department of Commerce, Bureau of the Census.