$[-/10$ Points$]$

ZillDiffEQModAp$123\mathrm{.}1\mathrm{.}011.$EP$.$

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.

Find the constant of proportionality $k,$ where $\frac{dl}{dt}=kl.$

$k=$

What is the intensity of the beam $18$ feet below the surface? $($Give your answer in terms of $I_0.$ Round any constants or coefficients to five decimal places.$)$