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 - Page 490: 106


75 ft The point (75,3) is on the graph of $f(x)$.

Work Step by Step

$f(x)=20(0.975)^{x}$ We want $f(x)=3$ (percent). Insert and solve for x: $ 3=20(0.975)^{x}\quad$...$/\div 20$ $\displaystyle \frac{3}{20}=0.975^{x}\qquad .../$apply ln() to both sides.. $\displaystyle \ln\frac{3}{20}=x\ln 0.975\quad$...$/\div\ln 0.975$ $ x=\displaystyle \frac{\ln\frac{3}{20}}{\ln 0.975}\approx$74.9322368691$\approx 75$ ft At about x = 75 ft depth, there is $ 3\%$ of surface sunlight . $\mathrm{f}(75)\approx 3$ The point (75,3) is on the graph of $f(x)$.
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