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

Francisca Rodden 2021-12-15 Answered
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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Expert Answer

Durst37
Answered 2021-12-16 Author has 37 answers

1LdL=k dx 
1LdL=k dx 
Power Fotmula: 1udu=ln|u|+C
ln|L|=kx+C
eln|L|=ekxC
L=Cekx
0,5=ek18
ln0.5=lne18k
ln0.5=18k
k=ln0.518
k0.0385
0.1=e0.0385x
ln0.1=lne0.0385x
ln0.1=0.0385
x=ln0.10.0385
k59.8 ft

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