Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set: 22

Answer

$t\approx-460.517$

Work Step by Step

Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the given equation, $ e^{-0.01t}=100 ,$ is \begin{array}{l}\require{cancel} \ln e^{-0.01t}=\ln100 \\\\ -0.01t(\ln e)=\ln100 \\\\ -0.01t(1)=\ln100 \\\\ -0.01t=\ln100 \\\\ t=\dfrac{\ln100}{-0.01} \\\\ t\approx-460.517 .\end{array}
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