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Thread: Calculus: Exponential Functions

  1. #1
    Deltaboy
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    Calculus: Exponential Functions

    can someone help me with this problem..



    well, I thought that f(x)= 2*e^(-x) was pretty close except when x at 2, y is not (2/9) but instead it's .5

    any one can help?
    thanks..
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Deltaboy View Post
    can someone help me with this problem..



    well, I thought that f(x)= 2*e^(-x) was pretty close except when x at 2, y is not (2/9) but instead it's .5

    any one can help?
    thanks..
    Well it goes through (0, 2), so
    $\displaystyle 2 = Ca^0 \implies C = 2$

    So the curve is $\displaystyle f(x) = 2a^x$.

    Again, the curve goes through $\displaystyle \left ( 2, \frac{2}{9} \right ) $ so,
    $\displaystyle \frac{2}{9} = 2a^2$

    $\displaystyle \frac{1}{9} = a^2$

    Thus
    $\displaystyle a = \pm \frac{1}{3}$

    Now, we may exclude the negative solution because the curve for this is, to put it mildly, psychotic. Thus
    $\displaystyle f(x) = 2 \left ( \frac{1}{3} \right ) ^x$

    -Dan
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