## College Algebra (6th Edition)

75 ft The point (75,3) is on the graph of $f(x)$.
$f(x)=20(0.975)^{x}$ 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 $f(x)$.