Question

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?

Answer 1

#$78.68 million.

Explanation:

Let wealth `w=ab^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 = 40b^8`. So, `b^8 = 11/8 and b = (11/8)^(1/8).= 1.0406`, nearly.
So, the model for wealth is
`w = 40((11/8)^(1/8))^y=40(1.0406)^y`, for approximation

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

Answer: $ 78.68 million, nearly. .