Consider a time-varying population that follows the logistic population model. The population has a limiting population of 800, and at time t = 0, its population of 200 is growing at a rate of 60 per year. a) Write a differential equation for the population P(t) that models this scenario. Solution: [Insert your math/explanation here.] b) Identify an appropriate solution technique and solve this differential equation. Solution: [Insert your math/explanation here.] c) Use MATLAB to plot your solution for t=0 to t = 10.