(Solved): [0/1 Points] ZILLDIFFEQMODAP12 3.1.011.EP. When a vertical beam of light passes through a transparen ...

[0/1 Points] ZILLDIFFEQMODAP12 3.1.011.EP. When a vertical beam of light passes through a transparent medium, the rate at which its intensity

decreases is proportional to

, where

represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is

of the initial intensity

of the incident beam. Find the constant of proportionality

, where

.

What is the intensity of the beam 13 feet below the surface? (Give your answer in terms of

. Round any constants or coefficients to five decimal places.)