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Thread: finding an exponential function

  1. September 22nd 2009, 12:11 PM #1
    kyleu03
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    finding an exponential function

    Find the exponential function f(x) = Cax whose graph is given.
    f(x) = 1




    any help with this?
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  2. September 22nd 2009, 01:18 PM #2
    redsoxfan325
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    Quote Originally Posted by kyleu03 View Post
    Find the exponential function f(x) = Cax whose graph is given.
    f(x) = 1




    any help with this?
    An exponential equation of this shape will have an equation f(x)=a(b^{-x}).

    Plugging in the two points gives us:

    2=a(b^{-0})
    \frac{2}{9}=a(b^{-2})

    Solve this system for a and b.

    Spoiler:
    Solving the first equation give us a=2. Plugging into the second equation gives us

    \frac{2}{9}=2(b^{-2})\implies \frac{1}{9}=b^{-2}\implies b=3.

    So the equation of the curve is f(x)=2(3^{-x}).
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