Chapter 1.5, Problem 18P

According to data from the U.S.Bureau of the Census, the population (measured in millions of people) of the U.S. in $1950$, $1960$, and $1970$ was, respectively, $151.3$, $179.4$, and $203.3$.

(a) Using the $1950$ and $1960$ population figures, solve the corresponding Malthusian population model.

(b) Determine the logistic model corresponding to the given data.

(c) On the same set of axes, plot the solution curves obtained in (a) and (b). From your plots, determine the values the different models would you have predicted for the population in $1980$ and $1990$, compare these predictions to the actual values of $226.54$ and $248.71$, respectively.