We saw in Section 4.1 how the logistic equation is used to describe a variety of things. Another example of logistic growth is shown in Fig. 17.14, which plots the density of a population of E. coli bacteria (Ram et al, 2019) as a function of time.

N(t) = 0.060 +
0.59 1 + e −
(t−4.2)
1.6 , where N is the mean cell density, and t is time in hours.

a. If we believe the logistic model, what will be the maximal cell density?

b. At what time does the maximal rate of growth occur, and what is it?
You have some complicated derivatives to work out. For goodness sake don’t do them by hand. It would take a week and you’d get them wrong anyway.

c. Compare your answer to the answer to Exercise 14.11. In that exercise you showed that the maximal rate of growth occurred at t = 0. Why is your answer different in this exercise?