Moonlight at High Noon
The fact that sunlight is absorbed by water is well known to any diver who has dived to a depth of 100 feet. It is also true that the intensity of light falls exponentially with depth. Suppose that at a depth of 25 feet the water absorbs 15% of the light that strikes the surface. At what depth would the light at noon be as bright as a full moon, which is one three-hundred-thousandth as bright as the noonday sun?
This is my work:
y = y(o) e^(kt)
.15 = 1 e^(25k)
ln(.15) = 25k
k = ln(.15)/25
1/300,000 = 1 e^[ln(.15)/25 * t]
t = 25/ln(.15) * ln(1/300,000)
What am I doing wrong here? I've gone over my work several times but I can't find my error and it's driving me crazy.
Did anyone else get this solution or is it indeed wrong?