\"I \"' " \"\"'\"' d \"" \""""" J \"V" "'" " \"' W' \"'1 \"'\""\"' V\" J ""' ""\" "\"' W' \"1 Exercise D. a) Approximate the area under the curve of the function f (X ) = 315 between X = 2 and X = 8 using a step size AX = 2. (Show your work) b) Compute the actual value of this area. Give your answer with two decimal places. Exercise E. The spread of a genetic mutation in a population of mice can be modeled by the differential equation P' : 3P(l P)(1 4P) where P is the fraction of the mice that have the new gene. (This means that 0 g P g l.) a) Find the equilibrium points of this model and determine the stability of each one. (You don't need to Check for number smaller than 0 or greater than 1). b) If 20% of the mice have the new gene initially (ie. P = 0.2), what fraction of the population will have the new gene in the long run? c) What if the initial fraction is 80% of the mice