# Suppose that the wealth of a business owner is increasing exponentially. In 1993, he had $40 million. In 2001, he had$55 million. How much money will he have in 2010?

Apr 8, 2016

$78.68 million. #### Explanation: Let wealth $w = a {b}^{y}$, Unit of w is$ 1 million and unit of y is 1 year.

Let y =0, at the start year 1993, and the wealth w= 40, then.

Using start conditions y = 0 and w = 40,
a = 40.

Using the corresponding values y = 2001-1993 = 8 and w = 55 then,
$55 = 40 {b}^{8}$. So, ${b}^{8} = \frac{11}{8} \mathmr{and} b = {\left(\frac{11}{8}\right)}^{\frac{1}{8}} . = 1.0406$, nearly.
So, the model for wealth is
$w = 40 {\left({\left(\frac{11}{8}\right)}^{\frac{1}{8}}\right)}^{y} = 40 {\left(1.0406\right)}^{y}$, for approximation

At 2010, y = 2010-1993 = 17. w then will be 40(1.04006)^17 = 78,68.

Answer: \$ 78.68 million, nearly. .