Logistic Growth In Chapter 6, the exponential growth equation was derived from the

Chapter 8, Problem 60

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Logistic Growth In Chapter 6, the exponential growth equation was derived from the assumption that the rate of growth was proportional to the existing quantity. In practice, there often exists some upper limit past which growth cannot occur. In such cases, you assume the rate of growth to be proportional not only to the existing quantity, but also to the difference between the existing quantity and the upper limit That is, In integral form, you can write this relationship as (a) A slope field for the differential equation is shown. Draw a possible solution to the differential equation if and another if To print an enlarged copy of the graph, select the MathGraph button. (b) Where is greater than 3, what is the sign of the slope of the solution? (c) For find (d) Evaluate the two given integrals and solve for as a function of where is the initial quantity. (e) Use the result of part (d) to find and graph the solutions in part (a). Use a graphing utility to graph the solutions and compare the results with the solutions in part (a). (f) The graph of the function is a logistic curve. Show that the rate of growth is maximum at the point of inflection, and that this occurs when