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OpenStudy (perl):
Suppose that rabbits are introduced onto an island where they have no natural enemies. Because of natural conditions, the island can support a maximum of 1000 rabbits. Let P(t) denote the number of rabbits at time t (measured in months), and suppose that the population varies in size (due to births and deaths) at a rate proportional to both P(t) and 1000 − P(t). That is, suppose that P(t) satisfies the differential equation dP/dt = kP(1000−P), where k is a positive constant. a) Find the value of P when the rate of change of the rabbit population is maximized.
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OpenStudy (perl):
b) When is the rate of change of the rabbit population a minimum? Discuss your answers.
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