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

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.