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Math Help - function of intensity

  1. #1
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    function of intensity

    the intensity of light, in lumens, passing through a liquid with an absorption coefficent of 0.2 is given by I(d)=100e^-0.2d, where d is the depth, in metres.
    a)what is the intensity of light passing through 5m of this liquid?
    b) how many metres must the light travel before the intensity is reduced to 1% of the original intensity?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by anitha View Post
    the intensity of light, in lumens, passing through a liquid with an absorption coefficent of 0.2 is given by I(d)=100e^-0.2d, where d is the depth, in metres.
    a)what is the intensity of light passing through 5m of this liquid?
    b) how many metres must the light travel before the intensity is reduced to 1% of the original intensity?
    For part (a), use a calculator:

    I(5)=100e^{-0.2(5)}=\dots

    For part (b):

    If the equation is I=I_0e^{-\alpha d}

    where

    I is the current intensity,
    I_0 is the original intensity, and
    \alpha is the absorption constant,

    we want to find the distance d where the current intensity is 1% of the original intensity, meaning that \frac{I}{I_0}=.01

    So the equation we want to solve is .01=e^{-0.2d}

    Taking the natural log of both sides gives us \ln(.01)=-0.2d\implies d=\frac{2\ln(10)}{0.2}\approx\dots

    I hope this makes sense!

    --Chris
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