# The intensity L(x) of light x feet beneath the surface of the ocean sa

The intensity L(x) of light x feet beneath the surface of the ocean satisfies the differential equation dL/dx = - kL, where k is a constant. As a diver you know from experience that diving to 18 ft in the Caribbean Sea cuts the intensity in half. You cannot work without artificial light when the intensity falls below a tenth of the surface value. About how deep can you expect to work without artificial light?
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Durst37

Power Fotmula: $\frac{1}{u}du=\mathrm{ln}|u|+C$
$\mathrm{ln}|L|=-kx+C$
${e}^{\mathrm{ln}|L|}={e}^{-kx\cdot C}$
$L=C{e}^{-kx}$
$0,5={e}^{-k\cdot 18}$
$\mathrm{ln}0.5={\mathrm{ln}e}^{-18k}$
$\mathrm{ln}0.5=-18k$
$k=-\frac{\mathrm{ln}0.5}{18}$
$k\approx 0.0385$
$0.1={e}^{-0.0385\cdot x}$
$\mathrm{ln}0.1={\mathrm{ln}e}^{-0.0385x}$
$\mathrm{ln}0.1=-0.0385$
$x=\frac{\mathrm{ln}0.1}{0.0385}$