Problem 2: Consider the following equation for a certain population of squirrels given by P P P P(t) (t is measured in years): (iit = 1.28 - P (1 E) (E 1) a. Find all the equilibrium points of the equations. b. Draw the phase line and determine the stability of each equilibrium points. c. Graph the Phase Plane with the 6 solution curves corresponding with the equilibriums solutions and the soltuions with initial conditions P(0) = 47 P(0) = 6 and P(O) = 12. d. At a certain time the hunting of squirrels become permitted and the law allows that a certain percentage oz of the squirrel population be eliminated every year. A new equation P P P for the squirrel population is then (flt = 1.28 - P (1 m) (E 1) aP The IALS (International Association for the Liberation of Squirrels) asserts than no more than 8% of squirrels should be eliminated every year (i.e a = 0.08, otherwise the popu lation would go extinct. On the contrary the UHA (United Hunters of America) asserts that it is safe to hunt 25% of the squirrel population every year (i.e. a = 0.25). i. Analyze the systems as a varies and determine who is right from the IALS or the UHA. ii. Find the largest possible value of 04 so that the squirrel population does not go extinct