Explanation Given information: Two bacteria strains: Suppose the population sizes of two strains of bacteria each grow as described by the recursions a t + 1 = R a a t and b t + 1 = R b b t , respectively. The frequency of the first strain at time t is defined as p t = a t / ( a t + b t ) . Calculation: Defined as p t = a t / ( a t + b t ) , the frequency of the first strain at t + 1 should be p t + 1 = a t + 1 a t + 1 + b t + 1 Realizing that a t + 1 = R a a t and b t + 1 = R b b t , then we have p t + 1 = R a a t R a a t + R b b t Dividing the numer . and the denom . by ( a t + b t ) = R a a t / ( a t + b t ) ( R a a t + R b b t ) / ( a t + b t ) = R a a t / ( a t + b t ) R a a t / ( a t + b t ) + R b b t / ( a t + b t ) Realizing that p t = a t / ( a t + b t ) = R a p t R a p t + R b b t a t + b t

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 1.6, Problem 39E

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To derive: a recursion for pt and show that it can be written in terms of a single constant α=Ra/Rb .

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Chapter 1.6, Problem 38E

Chapter 1.6, Problem 40E

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Chapter 1 Solutions

Biocalculus

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To derive: a recursion for p t and show that it can be written in terms of a single constant α = R a / R b .

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To derive: a recursion for pt and show that it can be written in terms of a single constant α=Ra/Rb .

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Chapter 1 Solutions