2. The hatchery was recently bought out by a corporation and the new owners are planning on allowing people to fish at the hatchery. So, the previous differential equation will no longer be a good prediction of the fish population at a given time. Below, find three possible differential equations that model the population of the fish in the hatchery, under the new assumption that people will be allowed to fish at the hatchery. Which of the three differential equations best models the new situation and why did you choose this one? (Assume the constant k represents the annual harvesting rate.) (a) dP dr - 2P (1-P) dt 25 - kP (b) dP=2P (1-P₂-k) dt 25 (c) d=2P (1-P)-k dt 25 Based on the differential equation you chose from Question 2, prepare a one page report for the CEO of the corporation that explains the implications that various choices of the annual harvesting rate k will have on future fish populations. You may include graphical representations in your report, but you must explain, in a concise way, the various effects the corporation's choice of the annual harvesting rate k will have on future fish populations.
2. The hatchery was recently bought out by a corporation and the new owners are planning on allowing people to fish at the hatchery. So, the previous differential equation will no longer be a good prediction of the fish population at a given time. Below, find three possible differential equations that model the population of the fish in the hatchery, under the new assumption that people will be allowed to fish at the hatchery. Which of the three differential equations best models the new situation and why did you choose this one? (Assume the constant k represents the annual harvesting rate.) (a) dP dr - 2P (1-P) dt 25 - kP (b) dP=2P (1-P₂-k) dt 25 (c) d=2P (1-P)-k dt 25 Based on the differential equation you chose from Question 2, prepare a one page report for the CEO of the corporation that explains the implications that various choices of the annual harvesting rate k will have on future fish populations. You may include graphical representations in your report, but you must explain, in a concise way, the various effects the corporation's choice of the annual harvesting rate k will have on future fish populations.
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
Transcribed Image Text:2. The hatchery was recently bought out by a corporation and the new owners are
planning on allowing people to fish at the hatchery. So, the previous differential
equation will no longer be a good prediction of the fish population at a given
time. Below, find three possible differential equations that model the population
of the fish in the hatchery, under the new assumption that people will be allowed
to fish at the hatchery. Which of the three differential equations best models
the new situation and why did you choose this one? (Assume the constant k
represents the annual harvesting rate.)
(a)
dP
dr - 2P (1-P)
dt
25
- kP
(b) dP=2P (1-P₂-k)
dt
25
(c)
d=2P (1-P)-k
dt
25
Based on the differential equation you chose from Question 2, prepare a one page
report for the CEO of the corporation that explains the implications that various
choices of the annual harvesting rate k will have on future fish populations. You
may include graphical representations in your report, but you must explain, in a
concise way, the various effects the corporation's choice of the annual harvesting
rate k will have on future fish populations.
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