It is estimated that x months from now, the population of a certain town will be changing at the rate of P'(x) = 2 + 1.5√x people per month. The current population is 5,000.

a. Find a function P(x) that satisfies these conditions. Use the graphing utility of your calculator to graph this function.

b. Use TRACE and ZOOM to determine the level of population 9 months from now. When will the population be 7,590?

c. Suppose the current population were 2,000 (instead of 5,000). Sketch the graph of P(x) with this assumption. Then sketch the graph of P(x) assuming current populations of 4,000 and 6,000. What is the difference between the graphs