A small town in Ohio commissioned an actuarial firm to conduct a study that modeled the rate of change of the town's population. The study found that the town's population (measured in thousands of people) can be modeled by the function P(t)= - 1/3t^3 +64t +300 , where tis measured in years.

a. Find the rate of change function P' (t) of the population function.
b. Find P '(1), P(2), P(3) and P' (4). Interpret what the results mean for the town.
c. Find P" (2), and P "(4). Interpret what the results mean for the town's population.