Explanation Given information: Ricker difference function with harvest included x t + 1 = c x t e − x t − h x t → is the population size at time t c → per capita reproductive output As t → ∞ the population size approaches to x The number of individuals are harvested in each time step is represented by h Formula used: Taylor’s series expansion: f ( x ) = f ( a ) + f ' ( a ) ( x − h ) + , , , , , , , , , , , Calculation: Consider the Ricker difference function x t + 1 = c x t e − x t From previous problem we have, The x in terms of the growth factor c is x = ln c x ( 0 ) = ln c The derivative of x with respect to h is x ' ( h ) = d x d h = 1 c ( 1 − x ) e − x

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ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3.8, Problem 4P

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To find: the linearization of x(h) at h=0.

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Chapter 3.8, Problem 3P

Chapter 3.8, Problem 5P

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Chapter 3 Solutions

Biocalculus

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the linearization of x ( h ) at h = 0.

Solution Summary: The author explains how the linearization of x(h) is =mathrmlnc-1

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Chapter 3 Solutions