College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4: 105

Answer

118 ft The point (118,1) is on the graph of $f(x)$.

Work Step by Step

$f(x)=20(0.975)^{x}$ We want $f(x)=1$ (percent). Insert and solve for x: $ 1=20(0.975)^{x}\quad$...$/\div 20$ $\displaystyle \frac{1}{20}=0.975^{x}\qquad .../$apply ln() to both sides... $\ln 0.05=x\ln 0.975\quad$...$/\div\ln 0.975$ $ x=\displaystyle \frac{\ln 0.05}{\ln 0.975}\approx$118.325104425$\approx 118$ ft At about x = 118 ft depth, there is $ 1\%$ of surface sunlight . $\mathrm{f}(118)\approx 1$ The point (118,1) is on the graph of $f(x)$.
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