Chapter 4.2, Problem 43E

Bacteria Population Assume that the total number (in millions) of bacteria present in a culture at a certain time $t$ (in hours) is given by

$N\left(t\right)=3t{\left(t-10\right)}^2+40.$

a. Find $N^{\text{'}}\left(t\right).$

Find the rate at which the population of bacteria is changing at the following times.

b. $8$ hours

c. $11$ hours

d. The answer in part b is negative, and the answer in part c is positive. What does this mean in terms of the population of bacteria?