A slope field for the logistic differential equation dy/dt=(1/2500)y(1010−y) is shown in the figure below. a. Sketch the solution curve that passes through the point (0,250), and sketch the solution curve that passes through the point (0,1500).
(i) If b=250, what is the largest rate of increase in the number of frogs in the pond? Explain your reasoning, and indicate units of measure.
(ii) 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.
b. Let b=100. Use Euler’s method, starting at t=0 with two steps of equal size, to approximate F(4), the number of frogs in the pond at time t=4 weeks. Show the work that leads to your answer.
c. Determine whether the approximation found in part (c) is an underestimate or an overestimate for the number of frogs in the pond at time t=4 weeks, when b=100. Explain your reasoning.