Question

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.

Answer 1

Answer: a) 389.915, b) 276.064.

Explanation:

Since we have given that

$P'(t)=20(0.95)^t$

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.

$\int\limits^\infty_0 {P'(t)} \, dt= \int\limits^\infty_0 {20(0.95)^t} \, dt=389.915$

(b) Find the amount after 24 hours.

It means 0<t < 24

$\int\limits^{24}_0 {P'(t)} \, dt= \int\limits^{24}_0 {20(0.95)^t} \, dt=276.064$

Hence, a) 389.915, b) 276.064.