Consider a fish species that is caught with nets. The growth of the fish stock in the absence of fishing is dy y - = 0.4y (1- 8000) dt and the harvest rate is, H = 0.001y (i) Determine the rate of increase of the fish stock when there is fishing. (ii) Solve for the fishing population, y, as a function of t. (iii) What will happen to the fish population as t → ∞? Justify your response.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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b) Consider a fish species that is caught with nets. The growth of the fish stock in the
absence of fishing is
dy
y
= 0.4y (1–
dt
8000-
and the harvest rate is, H= 0.001y
(i)
Determine the rate of increase of the fish stock when there is fishing.
(ii)
Solve for the fishing population, y, as a function of t.
(iii)
What will happen to the fish population as t → 0? Justify your response.
Transcribed Image Text:b) Consider a fish species that is caught with nets. The growth of the fish stock in the absence of fishing is dy y = 0.4y (1– dt 8000- and the harvest rate is, H= 0.001y (i) Determine the rate of increase of the fish stock when there is fishing. (ii) Solve for the fishing population, y, as a function of t. (iii) What will happen to the fish population as t → 0? Justify your response.
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