90. Sustainable Harvesting Suppose that a fish population evolves according to the logistic equation and that a fixed num- ber of fish per unit time are removed. That is, (1-2) dN = rN dt N - H K Assume that r = 2 and K = 1000. %3D (a) Find possible equilibria, and discuss their stability when H = 100. (b) What is the maximal harvesting rate that maintains a positive population size?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
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90. Sustainable Harvesting Suppose that a fish population
evolves according to the logistic equation and that a fixed num-
ber of fish per unit time are removed. That is,
dN
N
*(1-*)-
rN
dt
K
Assume that r=2 and K = 1000.
%3D
(a) Find possible equilibria, and discuss their stability when
H = 100.
%3D
(b) What is the maximal harvesting rate that maintains a positive
population size?
Transcribed Image Text:90. Sustainable Harvesting Suppose that a fish population evolves according to the logistic equation and that a fixed num- ber of fish per unit time are removed. That is, dN N *(1-*)- rN dt K Assume that r=2 and K = 1000. %3D (a) Find possible equilibria, and discuss their stability when H = 100. %3D (b) What is the maximal harvesting rate that maintains a positive population size?
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