A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by dP = kP – h, dt where k and h are positive constants. (a) Solve the DE subject to P(0) = Po. P(t) =
A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by dP = kP – h, dt where k and h are positive constants. (a) Solve the DE subject to P(0) = Po. P(t) =
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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![A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by
\[
\frac{dP}{dt} = kP - h,
\]
where \( k \) and \( h \) are positive constants.
(a) Solve the differential equation subject to \( P(0) = P_0 \).
\[ P(t) = \boxed{\phantom{some solution}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89f23a67-e2bf-44a3-9c56-ea6f97563460%2Ff8d54348-8dc0-4c59-a802-edf85878825a%2Fcxyf39_processed.png&w=3840&q=75)
Transcribed Image Text:A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by
\[
\frac{dP}{dt} = kP - h,
\]
where \( k \) and \( h \) are positive constants.
(a) Solve the differential equation subject to \( P(0) = P_0 \).
\[ P(t) = \boxed{\phantom{some solution}} \]
![**Instruction for Determining Fish Population Extinction**
Use the results from part (b) to determine whether the fish population will ever go extinct in finite time; that is, whether there exists a time \( T > 0 \) such that \( P(T) = 0 \). If the population goes extinct, then find \( T \). (If the population does not go extinct, enter DNE.)
\[ T = \text{[Input Box]} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89f23a67-e2bf-44a3-9c56-ea6f97563460%2Ff8d54348-8dc0-4c59-a802-edf85878825a%2Fhc5rs9_processed.png&w=3840&q=75)
Transcribed Image Text:**Instruction for Determining Fish Population Extinction**
Use the results from part (b) to determine whether the fish population will ever go extinct in finite time; that is, whether there exists a time \( T > 0 \) such that \( P(T) = 0 \). If the population goes extinct, then find \( T \). (If the population does not go extinct, enter DNE.)
\[ T = \text{[Input Box]} \]
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