Consider the following model of a population in continuous time. N(t) = rN(t)e¯ẞN(t), r > 0,ß> 0. (1) (a) Without solving the equation, determine an upper bound for N(t) in terms of the initial popu- lation No, and the parameters ẞ and r. (b) Suppose this population is subject to constant effort (proportional) harvesting with effort E > 0. 1. Find a condition on E for the harvested system to have a positive equilibrium N* and write down an expression for the yield at N* as a function of E. 2. Hence, determine the maximal sustainable yield for the harvested system.

Consider the following model of a population in continuous time. N(t) = rN(t)e¯ẞN(t), r > 0,ß> 0. (1) (a) Without solving the equation, determine an upper bound for N(t) in terms of the initial popu- lation No, and the parameters ẞ and r. (b) Suppose this population is subject to constant effort (proportional) harvesting with effort E > 0. 1. Find a condition on E for the harvested system to have a positive equilibrium N* and write down an expression for the yield at N* as a function of E. 2. Hence, determine the maximal sustainable yield for the harvested system.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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