An experimental garden plot contains N annual plants, each of which produces S seeds that are dropped

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An experimental garden plot contains N annual plants, each of which produces S seeds that are dropped within the same plot. A botanical model measures the number of offspring plants A(N) that survive until the next year by the function


image


where c and p are positive constants.


a. For what value of N is A(N) maximized? What is the maximum value? Express your answer in terms of S, c, and p.


b. For what value of N is the offspring survival rate A'(N) minimized?


c. The function


image


is called the net reproductive rate. It measures the number of surviving offspring per plant. Find F'(N), and use it to show that the greater the number of plants, the lower the number of surviving offspring per plant. This is called the principle of density-dependent mortality.

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Calculus For Business, Economics And The Social And Life Sciences

ISBN: 9780073532387

11th Brief Edition

Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price

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