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 planningto issue hunting permits to control the deer population (one deer perpermit). 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 capacityM, the population will decrease back to M through disease and malnutrition.a. Discuss the reasonableness of the following model for the growth rateof the deer population as a function of time:dP==rP(M-P)(Pm)dtwhere P is the population of the deer and r is a positive constant ofproportionality. Include a phase line.b. Explain how this model differs from the logistic modeldP=rP(M-P)dtIs 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 theequilibrium points of the model? Explain the dependence of the steady-state value of P on the initial values of P. About how many permits shouldbe issued?

Answered: Image /qna-images/answer/85a7e5c6-a0d3-4ae6-8250-364a0b6dc6f4.jpg

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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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?

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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