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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