A population grows at a rate P'(t) = 500te where P(t) is the population after t months. (a) Find a formula for the population size after t months, given that the population is 5000 at t = 0. (b) Use the answer from part (a) to find the size of the population after 6 months. (a) P(t) = (Type an exact answer in terms of e.) (b) The size of the population after 6 months is about (Round to the nearest person as needed.)