A biologist is studying the growth of a bacterial culture in a lab. The graph shows that bacteria's population $P$ varies with time $t$. At what time is the rate of growth of the bacterial population the greatest?

Given a function $H\left(t\right)$ that models the height (in centimeters) of a plant $t$ days after it was planted, estimate $H^{\prime }\left(90\right)$ from the provided graph. What does this derivative indicate?

Given four graphs of functions labeled I-IV and four graphs of their derivatives labeled A-D, match the graph of each function with its corresponding derivative graph.