4. (10 points) The number of frogs living in a pond at time t is modeled by the function y = F(t) that satisfies the logistic differential equation dy dt 25009(1010 - y) where t is measured in weeks. The number of frogs in the pond at time t = 0 is F(0) = b, where b is a positive constant. (a) (5 points) A slope field for the logistic differential equation is shown in the figure below. Sketch the solution curve that passes through the point (0, 250), and sketch the solution curve that passes through the point (0, 1500). 1500- 1250- 1000 750 500- 250- 20 30 40 (b) (5 points) If b = 250, what is the largest rate of increase in the number of frogs in the pond? If b = 750, what is the largest rate of increase in the number of frogs in the pond? Explain your reasoning, and indicate units of measure