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Exponential function problem

  1. Sep 20, 2009 #1
    I have a problem with an exponential function. I am wondering if an exact solution is possible, or if I have to write the solution as a logarithm of an unknown.

    A formula says that [tex]E(z)=E(0)^{-kz}[/tex], where E is light intensity and z is depth in water. My objective is to find the constant k. I also know that [tex]E(3)=0.01E(0)[/tex].

    I have tried to solve for k in the following way:

    [tex]E(3)=0.01E(0)[/tex]

    [tex]E(3)=100E(3)^{-3k}[/tex]
    [tex]\ln |0.01E(3)|=-3k \ln|E(3)|[/tex]

    I realize that all values except for k is a constant, however, I do not know the value of E, and my question is: Are there any ways to eliminate E(3) from the equation, leaving k=numerical constant?

    -dragonblood
     
  2. jcsd
  3. Sep 20, 2009 #2

    sylas

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    Science Advisor

    The formula you have is Beer's law, and E(z) is the intensity of light at a given depth. E0 is the input intensity, or intensity at depth 0.

    In your post, you have omitted the all important "e". The relation would normally be given as follows:

    [tex]E(z) = E_0 e^{-kz}[/tex]​

    You should be able to solve this for k, given E(3) = 0.01 E(0).

    Cheers -- sylas
     
  4. Sep 20, 2009 #3
    Thanks!
     
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