ZillDiffEQ$93\mathrm{.}1\mathrm{.}009.$When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I$($t$),$where t represents the thickness of the medium $($in feet$).$ In clear seawater, the intensity $3$ feet below the surface is $25\%$ of the initial intensity I$0$ of the incident beam. What is the intensity of the beam $14$ feet below the surface? $($Give your answer in terms of I$0.$ Round any constants or coefficients to five decimal places.$)$