1. Let pt denote the size of the U.S. population (in millions) at time t. Suppose the population increases by p percent per year. Let p0 denote the size of the population at time 0. Let p0 = 300 million.

(a) Write the expression for pt as a function of p0, p, and t. Show every step of all calculations.

(b) Use the expression in part (a) to compute the size of the population at time t = 5 if p = 3 percent. Show every step of all calculations.

(c) Calculate exactly how many years it will take for the population to increase to 600 million if p = 3 percent. Show every step of all calculations.

(d) Suppose the population increased from 300 million at time t = 0 to 360 million at time t = 20. Calculate the average population growth rate between those two time periods. Show every step of all calculations. (e) Let p0 = 300 million and p = 3 percent. Plot the size of the population on a standard scale when you let time t go from 0 to 30 on the horizontal axis.

(f) Make the same graph on a ratio scale.