Let represent sales of a new product (in thousands of
Chapter , Problem 3(choose chapter or problem)
Let represent sales of a new product (in thousands of units), let represent the maximum level of sales (in thousands of units), and let represent time (in months). The rate of change of with respect to varies jointly as the product of and (a) Write the differential equation for the sales model if when and when Verify that (b) At what time is the growth in sales increasing most rapidly? (c) Use a graphing utility to graph the sales function. (d) Sketch the solution from part (a) on the slope field shown in the figure below. To print an enlarged copy of the graph, go to the website www.mathgraphs.com.(e) If the estimated maximum level of sales is correct, use the slope field to describe the shape of the solution curves for sales if, at some period of time, sales exceed
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