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5. (12 points) Another example of a differential equation is the following: the population, P(t), of a certain species native to Houston - Instructorus Mathematicae - changes depending on time, t. Specifically, the rate of change in population is proportional to the population level with constant of proportionality given by 3. In other words, P' (t) = 3P(t ). (A) (5 points) Show that the function P(t) = 8est satisfies the differential equation above with initial condition P(0) = 8. (B) (2 points) What is the initial rate of change in the population level of Instructorus Mathematicae (i.e. what is the rate of change when t = 0?) (C) (3 points) What is the rate of change in the population level of Instructorus Mathematicae at the point in time when the population is P = 33