Chapter 2, Problem 94RE

Marine biology. The intensity of light entering water is reduced according to the exponential equation

$I=I_0{e}^{-kd}$

where $I$ is the intensity $d$ feet below the surface, $I_0$ is the intensity at the surface, and $k$ is the coefficient of extinction. Measurements in the Sargasso Sea have indicated that half of the surface light reaches a depth of $73.6$ feet. Find $k$ (to five decimal places), and find the depth (to

the nearest foot) at which $1\%$ of the surface light remains.