The Gompertz equation is N(t) = N0e A (1e t ) , for some (positive) constants

The Gompertz equation is N(t) = N0e A

α

(1−e

−αt

)

, for some (positive) constants N0, A and α

a. Calculate N 0 (t) and N 00(t).

b. As you will learn in Chapter 17, the maximum of N 0 is at a place where N 00 = 0. Use this fact to determine when the maximal rate of growth occurs. Show that the maximal rate of growth is αN0e A α
−1 .

c. Just as in Exercise 12.18 construct a Gompertz function and a logistic function that have the same initial population and maximal population. Compare the rates of growth in these two models. Discuss the scientific implications.