Question

A lens used to observe a solar eclipse will filter 69% of the sunlight entering the lens for each 10 millimeters in thickness. Find an exponential function for the percentage of sunlight S passing through the lens as a function of the thickness t (in mm) of the lens.

S=

Answer 1

hmmm let's reword it

what is the Decay equation for sunlight, decaying at 69% at every interval of 10 mm of thickness for "t"?

`\textit{Periodic/Cyclical Exponential Decay} \\\\ A=(1 - r)^{(t)/(c)}\qquad \begin{cases} A=\textit{current amount}\\ r=rate\to 69\%\to (69)/(100)\dotfill &0.69\\ t=thickness\\ c=period\dotfill &10 \end{cases} \\\\\\ A=(1 - 0.69)^{(t)/(10)}\implies A=0.31^{(t)/(10)}\hspace{5em}\boxed{S=0.31^{(t)/(10)}}`