A conservation organization releases 35 Florida panthers into a game preserve. After 3 years, there are 170 panthers in the preserve. The Florida preserve has a carrying capacity of 560 panthers. (a) Write a logistic equation that models the population of panthers in the preserve. (Round your k to four decimal places. Use t for the time In years.) (b) Find the population after 5 years. (Round your answer to the nearest whole number.) S panthers (c) When will the population reach 230? (Round your answer to two decimal places.) :vr (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. (Round your answer to the nearest whole number.) LE dt P6) =:] (e) At what time is the panther population growing most rapidly? (Round your answer to two decimal places.) :Jvr