# Thread: [SOLVED] Exponential Decay quick question

1. ## [SOLVED] Exponential Decay quick question

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?

2. Okay so I figured out what I did wrong after nearly losing my mind. If 15% of the light is absorbed, then 85% is left.
I didn't catch this.