Chapter 5.7, Problem 54E

Population Growth. An initial population of 70 bacteria is growing continuously at a rate of 2.5% per hour.

a. Write the differential equation that represents $P\left(t\right),$ the population of bacteria after t hours.

b. Find the particular solution of the differential equation from part (a).

c. Find $P\left(24\right)$ and $P\text{'}\left(24\right)$.

d. Find $P^{\prime }\left(24\right)/P\left(24\right)$, and explain what this number represents.