Answer: Another model for a growth function for a limited population is given by the
Chapter 9, Problem 20(choose chapter or problem)
Another model for a growth function for a limited population is given by the Gompertz function, which is a solution of the differential equation where is a constant and is the carrying capacity. (a) Solve this differential equation. (b) Compute . (c) Graph the Gompertz growth function for , , and , and compare it with the logistic function in Example 2. What are the similarities? What are the differences? (d) We know from Exercise 11 that the logistic function grows fastest when . Use the Gompertz differential equation to show that the Gompertz function grows fastest when
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