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Math Help - Find an exponential equation in the form f(x) = Pa^x given two points.

  1. #1
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    Find an exponential equation in the form f(x) = Pa^x given two points.

    If f(0) = 5 and f(6) = 23, using the form f(x) = Pa^x, find the value of P, and then find the value of a.

    So far, I have:

    f(6) = Pa^6 = 23
    P = 23/a^6

    Then I try to solve for a:

    f(0) = Pa^0 = 5

    Is this the right way to go about things? If I plug in my value for P I get:

    (23/a^6)*a^0 = 5
    (23/a^6)*1 = 5
    (23/a^6)*1 = 5
    23/5 = a^6


    Is this the right process? Now how do I solve for a?
    log 23/5 = 6 log a ??
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  2. #2
    MHF Contributor
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    Yes

    a^6 = \frac{23}{5}

    a = \left(\frac{23}{5}\right)^{\frac16}
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