Models of Population GrowthControlling a population The

Chapter 9, Problem 14E

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Problem 14EModels of Population GrowthControlling a population The fish and game department in a certain state is planning to issue hunting permits to control the deer population (one deer per permit). It is known that if the deer population falls below a certain level m, the deer will become extinct. It is also known that if the deer population rises above the carrying capacity M, the population will decrease back to M through disease and malnutrition.a. Discuss the reasonableness of the following model for the growth rate of the deer population as a function of time:b. Explain how this model differs from the logistic model dP/dt = rP(M P). Is it better or worse than the logistic model?c. Show that if P > M for all t, then d. What happens if P < m for all t ?e. Discuss the solutions to the differential equation. What are the equilibrium points of the model? Explain the dependence of the steady-state value of P on the initial values of P. About how many permits should be issued?

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