Suppose a population, P(t), of deer satisfies the logistic equation with harvesting given below, where t is in months. (You do not need to find P(t) exactly to answer these

questions) \frac{d P}{d t}=0.02 P(500-P)-h a) With h = 0, what is the carrying capacity of the system? Sketch likely solutions curves both above and below the carrying capacity. b) Let h = 300 represent that 300 deer are hunted each month. What are the new critical points? Draw a new phase diagram and determine whether the new equilibrium solutions are stable, unstable, or semi-stable. c) What is the long term behavior of the deer population with h= 300 if the initial population is 100 deer?