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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?

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?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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please solve the last part, 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?

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: dP = =rP(M-P)(Pm) dt where P is the population of the deer and r is a positive constant of proportionality. Include a phase line. b. Explain how this model differs from the logistic model dP =rP(M-P) dt Is it better or worse than the logistic model? c. What happens if P > M for all t? 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?
Transcribed Image Text: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: dP = =rP(M-P)(Pm) dt where P is the population of the deer and r is a positive constant of proportionality. Include a phase line. b. Explain how this model differs from the logistic model dP =rP(M-P) dt Is it better or worse than the logistic model? c. What happens if P > M for all t? 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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