please solve parts c and d 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?

Given that the fish and game department in a certain state is planning to issue hunting permits to…

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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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Question

please solve parts c and d

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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