Solution: In a fish farm, a population of fish is introduced into a pond and harvested
Chapter 3, Problem 38(choose chapter or problem)
In a fish farm, a population of fish is introduced into a pond and harvested regularly. A model for the rate of change of the fish population is given by the equation dP dt r0S1 2 Pstd Pc DPstd 2 Pstd where r0 is the birth rate of the fish, Pc is the maximum population that the pond can sustain (called the carrying capacity), and is the percentage of the population that is harvested. (a) What value of dPydt corresponds to a stable population? (b) If the pond can sustain 10,000 fish, the birth rate is 5%, and the harvesting rate is 4%, find the stable population level. (c) What happens if is raised to 5%?
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