For a certain endangered species, the goal is to have 400 breeding adults in the wild by 2023. If progress toward this goal continues, the population of breeding adults in the wild in year x can be approximated by P(x) = 73e0.11x, where x= 12 corresponds to the year 2012. Use this model to find the following. (a) P(14) (b) P'(x) and P'(14) (c) Interpret the answers in parts (a) and (b). (a) P(14) = (Round to the nearest integer as needed.)

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