# exponential modelling help

• February 23rd 2010, 05:48 PM
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.
• February 23rd 2010, 06:39 PM
NOX Andrew
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.

$x = 0.096$