A biologist is growing bacteria for a lab experiment. There are 10 mg of bacteria in a controlled environment when she changes the temperature. The amount P of bacteria then grows at a rate of P'(t) = 20(0.95)^t per hour where t is the number of hours since the temperature changed

(a) Write an integral that models the amount of bacteria at time t > 0.
(b) Find the amount after 24 hours.