Answer
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 $f(x)$.
