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Math Help - exponential modelling help

  1. #1
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    Feb 2010
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    Unhappy exponential modelling help

    What rate of interest compounded anually must an investment earn in order for $8000 to grow to $20 000 in 10 years?

    I have the beginning equation as 20 000 = 8000(1 + x)^{10} But I don't know how to solve for x, x being the interest rate as a decimal.
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  2. #2
    Member
    Joined
    Dec 2009
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    First, divide the equation by 8,000.

    \frac{5}{2} = (x + 1)^{10}

    From here, take the 10th root of the equation.

    \pm (\frac{5}{2})^{\frac{1}{10}} = x + 1

    Subtract 1 from the equation.

    -1 \pm (\frac{5}{2})^{\frac{1}{10}} = x

    You can use a calculator to find a decimal approximation of the expression on the right.

    -1 \pm 1.096 = x

    x = \{-2.096, 0.096\}

    In the context of the problem, we can ignore the negative answer.

    x = 0.096
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