Chapter 8.2, Problem 29ES

Suppose that an initial population of 10,000 bacteria grows exponentially at a rate of $2\%$ per hour and that $y=y(t)$ is the number of bacteria present t hours later.

(a) Find an initial-value problem whose solution is $y(t).$

(b) Find a formula for $y\left(t\right).$

(c) How long does it take for the initial population of bacteria to double?

(d) How long does it take for the population of bacteria to reach 45,000?