Gompertz model: One possible substitute for the logistic model of population growth is the Gompertz model, according to which For simplicity in this problem we take r = 1, so this reduces to a. Let K...

Gompertz model: One possible substitute for the logistic model of population growth is the Gompertz model, according to which

For simplicity in this problem we take r = 1, so this reduces to

a. Let K = 10, and make a graph of the rate of growth versus N for the Gompertz model.

b. Use the graph you obtained in part a to determine for what value of N the growth rate reaches its maximum. This is the optimum yield level under the Gompertz model with K = 10.

c. Under the logistic model the optimum yield level is K/2. What do you think is the optimum yield level in terms of K under the Gompertz model? (Hint: Repeat the procedure in parts a and b using different values of K, such as K = 1 and K = 100. Try to find a pattern.)