Suppose that the growth-rate parameter k = 0.3 and the carrying capacity N = 2500 in the logistic population model of Exercise 17. Suppose P(0) = 2500. (a) If 100 fish are harvested each year, what does the model predict for the longterm behavior of the fish population? In other words, what does a qualitative analysis of the model yield? (b) If one-third of the fish are harvested each year, what does the model predict for the long-term behavior of the fish population?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
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Suppose that the growth-rate parameter k = 0.3 and the carrying capacity N = 2500
in the logistic population model of Exercise 17. Suppose P(0) = 2500.
(a) If 100 fish are harvested each year, what does the model predict for the longterm
behavior of the fish population? In other words, what does a qualitative
analysis of the model yield?
(b) If one-third of the fish are harvested each year, what does the model predict for
the long-term behavior of the fish population?

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