Suppose that the growth-rate parameter k = 0.3 and the carrying capacity N = 2500 in the logistic population model of Exercise 1. 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?
Exercise 1
Suppose a species of fish in a particular lake has a population that is modeled by the logistic population model with growth rate k, carrying capacity N, and time t measured in years. Adjust the model to account for each of the following situations.
(a) One hundred fish are harvested each year.
(b) One-third of the fish population is harvested annually.
(c) The number of fish harvested each year is proportional to the square root of the number of fish in the lake.
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