Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter D1.4, Problem 41E

Optimal harvesting rate Let y(t) be the population of a species that is being harvested, for t ≥ 0. Consider the harvesting model y′(t) = 0.008y – h, y(0) = y₀, where h is the annual harvesting rate, y₀ is the initial population of the species, and t is measured in years.

a. If y₀ ⁼ 2000, what harvesting rate should he used to maintain a constant population of y = 2000, for t ≥ 0?

b. If the harvesting rate is h = 200/year, what initial population ensures a constant population?

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Chapter D1.4, Problem 40E

Chapter D1.4, Problem 42E

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Chapter D1 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. D1.1 - Prob. 1E Ch. D1.1 - Prob. 2E Ch. D1.1 - Prob. 3E Ch. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...

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Solution Summary: The author calculates the harvesting rate of a given model, based on the steady state solution of y=25,000.

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