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Suppose that the equation dr = kr(M – x) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax %3D 2

Suppose that the equation dr = kr(M – x) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax %3D 2

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...
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Suppose that the equation dr = kr(M – 1) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax 2 (d) If E 2 kM, show that r(t) → 0 as t → x, that is the lake is eventually fished out.
Transcribed Image Text:Suppose that the equation dr = kr(M – 1) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax 2 (d) If E 2 kM, show that r(t) → 0 as t → x, that is the lake is eventually fished out.
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