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Math Help - [SOLVED] Exponential Decay quick question

  1. #1
    Jul 2009

    [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?
    Last edited by FZ44; July 28th 2009 at 10:58 PM.
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  2. #2
    Jul 2009
    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.
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