EXAMPLE 4 Logistic population growth Assume 50 fruit flies are in a large jar at the beginning of an experiment. Let P(t) be the number of fruit flies in the jar t days later. At first, the population grows exponentially, but due to limited space and food supply, the growth rate decreases and the population is prevented from growing without bound. This experiment is modeled by the logistic equation – 0.10(1 - P ,for t > 0, 300, dP dt together with the initial condition P(0) = 50. Solve this initial value problem.

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