Suppose that a population develops according to the logistic equation dP dt = 0.06P − 0.0006P2, where t is measured in weeks. (a) What is the carrying capacity? M =  What is the value of k? k =  (b) A direction field for this equation is shown in the figure below. On the coordinate plane the horizontal axis is labeled t and the vertical axis is labeled P. There is a slope field in the first quadrant on the graph. The slopes are nearly horizontal at P = 0. As P increases, the slopes go up and right becoming more steep until about P = 50, then go up and right becoming less steep, become horizontal near P = 100, and go down and right becoming more steep until they exit the window near P = 150. Where are the slopes close to 0? (Enter your answers as a comma-separated list.) P =        Where are the slopes largest? (Enter your answers as a comma-separated list.) P =        Which solutions are increasing? (Enter your answer using interval notation.) P0 ∈        Which solutions are decreasing? (Enter your answer using interval notation.) P0 ∈

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