A conservation organization releases 25 Florida panthers into a game preserve. After 2 years, there are 39 panthers in the preserve. The Florida preserve has a carrying capacity of 200 panthers.
(a) Write a logistic equation that models the population of panthers in the preserve.
(b) Find the population after 5 years.
(c) When will the population reach 100?

(d) Write a logistic differential equation that models the growth rate of the panther population. Then repeat part (b) using Euler's Method with a step size of h = 1. Compare the approximation with the exact answer.

(e) At what time is the panther population growing most rapidly? Explain.