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 · Accepted Answer

1LdL=−k&amp;nbsp;dx&amp;nbsp;∫1LdL=−∫k&amp;nbsp;dx&amp;nbsp;Power Fotmula:&amp;nbsp;1udu=ln|u|+Cln|L|=−kx+Celn|L|=e−kx⋅CL=Ce−kx0,5=e−k⋅18ln⁡0.5=ln⁡e−18kln⁡0.5=−18kk=−ln⁡0.518k≈0.03850.1=e−0.0385⋅xln⁡0.1=ln⁡e−0.0385xln⁡0.1=−0.0385x=ln⁡0.10.0385k≈59.8&amp;nbsp;ft

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

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