Find a formula for P(t) in Exercise 17 if, initially, 10,000 bacteria were present in the culture.

Exercise 17

In an experiment, a certain type of bacteria was being added to a culture at the rate of e^0.03t + 2 thousand bacteria per hour. Suppose that the bacteria grow at a rate proportional to the size of the culture at time t, with constant of proportionality k = .45. Let P(t) denote the number of bacteria in the culture at time t. Find a differential equation satisfied by P(t).