As we saw in Exercise 4.23 the Gompertz equation, N(t) = N0e A (1e t )

As we saw in Exercise 4.23 the Gompertz equation, N(t) = N0e A

α

(1−e

−αt

)

,

can be used to model growing populations. Here, N is the number in the population, and A, N0 and α are positive constants.

a. Calculate the maximal population in the Gompertz equation.

b. Now, compare the shape of the Gompertz equation to the shape of the logistic equation of the previous question.
Choose parameters so that the initial population in each equation is 1000, and the maximal population is 106 . Then, plot the Gompertz and logistic equations on the same graph to see how the shapes differ. Can you choose the parameters of the Gompertz equation to make it look exactly like the logistic equation? Discuss the scientific implications.