Assume there is a certain population of deer in a forest whose growth is described by the logistic equation. The constant of proportionality for this type of deer is k = 0.57, and the carrying capacity of the forest is 10,000 deer. If the starting population is 7400 deer, then after one breeding season the population of the forest is

Suppose that a particular plot of land can sustain 500 deer and that the population of this particular species of deer can be modeled according to the logistic model as dPdt=0.2(1P500)P. Each year, a proportion of the herd deer is sold to petting zoos. a. Find the function that gives the equilibrium population for various proportions. b. Determine the maximum number of deer that should be sold to petting zoos each year. Hint: Find the maximum sustainable harvest