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.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 2EA
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Transcribed Image Text: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.
Transcribed Image Text:Determine the maximal sustainable harvest rate. (This is the maximal h for which the population
does not decrease with time).
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