Chapter 4.2, Problem 18E

Reminder Round all answers to two decimal places unless otherwise indicated.

The Beer-Lambert-Bouguer Law When light strikes the surface of a medium such as water or glass, its intensity decreases with depth. The Beer-Lambert-Bouguer law states that the percentage of decrease is the same for each additional unit of depth. In a certain lake, intensity decreases about $75\%$ for each additional meter of depth.

a.	Explain why intensity $I$ is an exponential function of depth $d$ in meters.
b.	Use a formula to express intensity $I$ as an exponential function of $d$. (Use $I_{\text{o}}$ to denote the initial intensity.)
c.	Explain in practical terms the meaning of $I_{\text{o}}$.
d.	At what depth will the intensity of light be one-tenth of the intensity of light striking the surface?