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Math Help - Exponential Function

  1. #1
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    Exponential Function

    I have two here.

    a=b(e^(-c))
    solve for c

    For that one, I have looked around and tried to figure it out and all i can think is that I need to use Log to solve it.

    a=b/(c^2)
    explain what happens to the value of a if c is doubled.
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  2. #2
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    a = b\,e^{-c}

    \frac{a}{b} = e^{-c}

    \ln{\left(\frac{a}{b}\right)} = -c

    c = -\ln{\left(\frac{a}{b}\right)}.
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  3. #3
    MHF Contributor Unknown008's Avatar
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    For the second one, can take the sign of proportionality.

    a = \frac{b}{c^2}

    a\ \alpha\ \frac{1}{c^2}

    If c doubles, then;

    So, if a becomes a' and c becomes c', it becomes:

    a'\ \alpha\ \frac{1}{c'^2}

    Now, we know that c' = 2c.

    a'\ \alpha\ \frac{1}{(2c)^2}

    a'\ \alpha\ \frac{1}{4c^2}

    4a'\ \alpha\ \frac{1}{c^2}

    So, a = 4a' and hence, a/4 = a'. You conclude that the new a' is quadrupled when compared to the previous a

    (here, c' means the new value of c, not the derivative of c.)

    [Note, until I find the sign for the proportionality, I'll use alpha instead]
    Last edited by Unknown008; August 23rd 2010 at 05:37 AM. Reason: Used a better approach for an explanation
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  4. #4
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    thank you very much
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