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t-Harvest Model A model that describes the population of a
Chapter 3, Problem 42E(choose chapter or problem)
Constant-Harvest Model A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by
\(\frac{d P}{d t}=k P-h\)
where k and h are positive constants.
(a) Solve the DE subject to \(P(0)=P_{0}\).
(b) Describe the behavior of the population P(t) for increasing time in the three cases \(P_{0}>h / k, P_{0}=h / k\), and \(0<P_{0}<h / k\).
(c) Use the results from part (b) to determine whether the fish population will ever go extinct in finit time, that is, whether there exists a time T > 0 such that P(T) = 0. If the population goes extinct, then find T.
Text Transcription:
P(0) = P_0.
P_0 > h/k, P_0 = h/k
0 < P_0 < h/k
Questions & Answers
QUESTION:
Constant-Harvest Model A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by
\(\frac{d P}{d t}=k P-h\)
where k and h are positive constants.
(a) Solve the DE subject to \(P(0)=P_{0}\).
(b) Describe the behavior of the population P(t) for increasing time in the three cases \(P_{0}>h / k, P_{0}=h / k\), and \(0<P_{0}<h / k\).
(c) Use the results from part (b) to determine whether the fish population will ever go extinct in finit time, that is, whether there exists a time T > 0 such that P(T) = 0. If the population goes extinct, then find T.
Text Transcription:
P(0) = P_0.
P_0 > h/k, P_0 = h/k
0 < P_0 < h/k
ANSWER:Step 1 of 4
In this problem, we have to solve the differential equation subject to
b) Explain the scenario when ,
.
c) We have to determine the fist population at finite time.