Question: A population of deer in a forest can be modeled using the equation dp/dt = aP (1 - P/N) - dP where P is the population in hundreds, a is the growth rate of the population, N is the carrying capacity of the forest and d is the proportional rate(%) at which deer are being hunted.
a. If a = 0.5 and N = 500, draw a phase line for 0% hunting, 25% hunting, 50% hunting, 75% hunting and 100% hunting.
b. Determine the value of d for which the percentage of hunting is too large to sustain the population.
c. If hunting is restricted to 10% and the initial population of deer is 150, describe what happens to the population in the long run.
d. Sketch a slope field with various initial populations (a portrait) for case of 10% hunting.