Explanation Given information: Insecticide resistance: If the frequency of a gene for insecticide resistance is p , then its frequency in the next generation is given by the expression p ( 1 + s ) 1 + s p where s is the reproductive advantage that this gene has over the wild type in the presence of the insecticide. Calculation: Let f ( s ) = p ( 1 + s ) 1 + s p be the frequency of a gene for insecticide resistance in the next generation as a function of s , where p is the frequency of the gene in the present generation; constant. Using the Quotient Rule , the rate at which the gene frequency in the next generation changes as s changes is f ' ( s ) = ( 1 + s p ) [ p ( 1 + s ) ] ' − p ( 1 + s ) ( 1 + p s ) ' ( 1 + s p ) 2 = ( 1 + s p ) [ p ( 0 + 1 ) ] − p ( 1

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.4, Problem 54E

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Chapter 3.4, Problem 53E

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Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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rate at which the gene frequency in the next generation changes as s changes.

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