Chapter 3, Problem 97RE

Light intensity. The Bouguer—Lambert Law states that the intensity $\text{I}$ of sunlight filtering down through water at a depth $x$ (in meters) decreases according to the exponential decay function ${\rm I}={{\rm I}}_0{e}^{-kx},$ where ${{\rm I}}_0$ is the intensity at the surface and $k>0$ is an absorption constant that depends on the murkiness of the water. Suppose the absorption constant of Carrollwood Lake was experimentally determined to be $k=0.73$. How much light has been absorbed by the water at a depth of $\text{2}$ meters?