Mathematics, 14.02.2020 05:51 olguita82
A special type of autonomous differential equation, called the logistic equation, is typically written as Cape = rP(1- ), and is used to model ecological populations P>0. The constant r is called the intrinstic growth rate. The constant K is the greater of two equilibrium solutions called the environmental carrying capacity, and is the maximum sustainable population that the environment can support. Suppose that a population develops according to the logistic equation: dP -= 0.15P - 0.0002P2, where t is measured in weeks. dt a. Rewrite the equation in the typical form to determine the intrinsiſ growth rate and environmental carrying capacity. Note: Since K is an equilibrium solution, it is can also be found by setting the right-hand-side of the equation equal to zero. b. For what values of P is the population increasing and decreasing? Write your answers in interval notation
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