150 100 50 20 40 60 3. Suppose that a population develops according to the logistic equation (c) Use the direction field to sketch solutions for initial pop- ulations of 20, 40, 60, 80, 120, and 140. What do these dP = 0.05P - 0.0005P2 dt solutions have in common? How do they differ? Which solutions have inflection points? At what population levels do they occur? (d) What are the equilibrium solutions? How are the other solutions related to these solutions? where t is measured in weeks. (a) What is the carrying capacity? What is the value of k? (b) A direction field for this equation is shown. Where are the slopes close to 0? Where are they largest? Which solutions are increasing? Which solutions are decreasing?

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