The fish and game department in a certain state is planning to issue hunting permits to control the deer population (one deer pe permit). It is known that if the deer population falls below a certain l the deer will become extinct. It is also known that if the de pulation above the ing
The fish and game department in a certain state is planning to issue hunting permits to control the deer population (one deer pe permit). It is known that if the deer population falls below a certain l the deer will become extinct. It is also known that if the de pulation above the ing
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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please solve part e (the last one)
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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