Explanation Given Information: Wolf population satisfies the formula given by, w ( t ) = 835 ( 1 − e − 2006 t ) Wolf population was first introduced in 1994 The initial time the wolf population was introduced the year 1994 can be taken as t = 0 Then, below formula can be used to find the rate of change in the given function over the time interval [0, t] The average rate of change = w ( t ) − w ( 0 ) t − 0 In order to approximate the rate of increase of wolves per year: To do so find the limit of the below. lim t → 0 w ( t ) t lim t → 0 835 ( 1 − e − 0.006 t ) t lim t → 0 − 835 ( − 0.006 ) e − 0.006 t 1 = − 835 ( − 0.006 ) ( 1 ) = − 835 ( − 0.006 ) ( 1 ) = 5.01 since this was the slope of the line between points ( t , w ( t ) ) and the origin

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.6, Problem 88A

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To Find: the limit of w(t)t as t→0

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Chapter 3.6, Problem 87A

Chapter 3.6, Problem 89A

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j) f) lim x+x ex g) lim Inx h) lim x-5 i) lim arctan x x700 lim arctanx 811x

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Chapter 3 Solutions

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