The spread of a genetic mutation in a population of mice can be modeled by the differential equation P = 2P (1 P) (1 3P) where P is the fraction of the mice that have the new gene. (This means that 0 P 1.) a) Find the equilibrium points of this model and determine the stability of each one. b) If 10% of the mice have the new gene (so P = 0.1) initially, what fraction of the population will have the new gene in the long run? c) What if the initial fraction is 90% of the mice?