A beam of light enters a medium such as water or smog with initial intensity I0. Its intensity decreases depending on the thickness (or concentration) of the medium. The intensity I at a depth (or concentration) of x units is given by
I = I0e-mx.
The constant m (the Greek letter "mu") is called the coefficient of absorption, and it varies with the medium. For sea water, μ = 1.4.
a) What percentage of light intensity I0 remains in sea water at a depth of 1 m? 3 m? 5 m? 50 m?
b) Plant life cannot exist below 10 m. What percentage of I0 remains at 10 m?