A company is considering to start harvesting salmon in a new region. They model the salmon population size in that region by the equation P' (t) = kP(t) — h, with the natural growth rate of k = 2 salmon per year per population and a harvest rate h salmon per year. The company wants to decide how much salmon to harvest per year. The company estimates that currently there is 1mil salmon in that region.
A company is considering to start harvesting salmon in a new region. They model the salmon population size in that region by the equation P' (t) = kP(t) — h, with the natural growth rate of k = 2 salmon per year per population and a harvest rate h salmon per year. The company wants to decide how much salmon to harvest per year. The company estimates that currently there is 1mil salmon in that region.
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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Transcribed Image Text:The text discusses a scenario involving different choices of harvest rates for a population of salmon. The goal is to determine the impact on the salmon population using a specified model. The harvest rates considered are:
(i) \(h = 500,000\),
(ii) \(h = 1 \text{ million}\),
(iii) \(h = 2 \text{ million}\),
(iv) \(h = 3 \text{ million}\).
![A company is considering starting to harvest salmon in a new region. They model the salmon population size in that region by the equation
\[ P'(t) = kP(t) - h, \]
with the natural growth rate of \( k = 2 \) salmon per year per population and a harvest rate \( h \) salmon per year. The company wants to decide how much salmon to harvest per year. The company estimates that currently there are 1 million salmon in that region.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeefd442-7c64-4a51-8ed1-c0196ac6a13e%2F1e2feea6-fedb-4f2c-8b5e-d41ceec26d7e%2Fquk0g7h_processed.png&w=3840&q=75)
Transcribed Image Text:A company is considering starting to harvest salmon in a new region. They model the salmon population size in that region by the equation
\[ P'(t) = kP(t) - h, \]
with the natural growth rate of \( k = 2 \) salmon per year per population and a harvest rate \( h \) salmon per year. The company wants to decide how much salmon to harvest per year. The company estimates that currently there are 1 million salmon in that region.
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