1. You will be constructing a slope field(a qualitative analysis) for the following scenario. Suppose that the population of weasels in a particular park is modeled by the differential equation (in thousands of weasels): dP .0153P(P-32) dt a. Find and draw any equilibrium solutions. b. Draw the isoclines for P=10 and P-40. Make sure you indicate the slopes for the isoclines. c. Indicate the areas where the solution curves are increasing and decreasing. d. Find the changes in concavity. Then determine the concavity of the functions e. Describe what will happen to the population if the population starts at 20,000 weasels. Draw a solution curve to demonstrate your findings.

Fig: 1