Starting with an initial value of P(0) = 20, the population of a prairie dog community grows at a rate of $P'(t) = 10 - \frac{t}{2}$ (in units of prairie dogs/month), for $0 \le t \le 20$. Set up the integral using Theorem 6.1, do not use the antiderivative method from section 4.9. Show all work for full credit.
a. Find the population P(t) for $0 \le t \le 20$.
b. What is the population 13 months later?
a. The population P(t) for $0 \le t \le 20$ is P(t) =
b. After 13 months, the population is prairie dogs.
(Type a whole number. Round to the nearest prairie dog as needed.)
