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 $f(x)$.
