1. Let pt denote the size of the U S. population (in millions) at time t. Suppose the population mcreases by 13 percent per year. Let p0 denote the size of the population}- at time 0. Let 190: 300 million. (a) Write the expression for pt as a function of m, p, and t. (Show every step of all calculations) " (b) Use the expression in part (a) to compute the Size of the population at tim6 ' 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. ShowIevery step of all calculations. ((1) 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