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Optimal harvesting rate Let y(t) be the population of a
Chapter 7, Problem 52E(choose chapter or problem)
Optimal harvesting rate Let y(t) be the population of a species that is being harvested. Consider the harvesting model \(y^{\prime}(t)=0.008 y-h\), \(y(0)=y_{0}\), where h > 0 is the annual harvesting rate and \(y_{0}\) is the initial population of the species.
a. If \(y_{0}=2000\), what harvesting rate should be used to maintain a constant population of y = 2000 for \(t \geq 0\)?
b. If the harvesting rate is h = 200/year, what initial population ensures a constant population for \(t \geq 0\)?
Questions & Answers
QUESTION:
Optimal harvesting rate Let y(t) be the population of a species that is being harvested. Consider the harvesting model \(y^{\prime}(t)=0.008 y-h\), \(y(0)=y_{0}\), where h > 0 is the annual harvesting rate and \(y_{0}\) is the initial population of the species.
a. If \(y_{0}=2000\), what harvesting rate should be used to maintain a constant population of y = 2000 for \(t \geq 0\)?
b. If the harvesting rate is h = 200/year, what initial population ensures a constant population for \(t \geq 0\)?
ANSWER:SOLUTIONStep 1 Let y(t) be the population of a species that is being harvested. Consider the harvesting model is the annual harvesting rate and is the initial population of the species.