Assume we are considering the survival of whales and that if the number of whales falls below a minimum survival level m, the species will become extinct. Assume also that the population is limited by the carrying capacity M of the environment. That is, if the whale population is above M, then it will experience a decline because the environment cannot sustain that high a population level.

a. Discuss the following model for the whale population:

b. Graph dP/dt versus P and P versus t. Consider the cases in which the initial population P (0) = P₀ satisfies P₀ 0 0.

c. Solve the model in part (a), assuming that m

d. Discuss how you would test the model in part (a). How would you determine M and m?

e. Assuming that the model reasonably estimates the whale population, what implications are suggested for fishing? What controls would you suggest?