Question: (a) On the slope field for dP/dt = 3P - 3P2 in Figure, sketch three solution curves showing different types of behavior for the population, P.
(b) Is there a stable value of the population? If so, what is it?
(c) Describe the meaning of the shape of the solution curves for the population: Where is P increasing? Decreasing? What happens in the long run? Are there any inflection points? Where? What do they mean for the population?
(d) Sketch a graph of dP /dt against P. Where is dP /dt positive? Negative? Zero? Maximum? How do your observations about dP /dt explain the shapes of your solution curves?
