Question: Problem 5. Solve the following initial value problem for the logistic equation:dPdt rP p1 PK q (2)P p0q K{2.This represents the growth of a population

Problem 5. Solve the following initial value problem for the logistic equation:dPdt rP p1 PK q (2)P p0q K{2.This represents the growth of a population whose initial value is half the carrying capacity ofthe environment.A population of rabbits is though to evolve according to (2). The carrying capacity is knownto be 500 rabbits, and the growth rate 0.04 rabbits/month. If the initial population is 250rabbits, what does the model predict the population to be after 1 year?

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