SOLUTION: A pair of women's running shoes cost $110 in 2004 and the same shoes cost $130 in 2009 due to inflation. a. Develop an exponential model to describe the rate of inflation over thi

Question 1100351: A pair of women's running shoes cost $110 in 2004 and the same shoes cost $130 in 2009 due to inflation.
a. Develop an exponential model to describe the rate of inflation over this time period.
b. If inflation continues at the same; rate, use your model in part; (a) to estimate the price of the shoes in 2016.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
shoes cost 110 in 2004.
same shoes cost 130 in 2009.

2009 - 2004 = 5
130 = 110 * (1 + r) ^ 5
divide both sides of the equation by 110 to get:
130/110 = (1 + r) ^ 5
take the fifth root of both sides of the equation to get:
(130/110)^(1/5) = 1 + r
solve for r to get:
r = (130/110)^(1/5) - 1 = .033975227

that's your average annual exponential growth rate of inflation.

in 2009, at the present rate of inflation from 2004, the shoes will cost 110 * (1.033975227) ^ 5 = 130.

in 2016, at the present rate of inflation from 2004, the shoes will cost (110 * (1.033975227) ^ 12 = 164.2533691

2009 is 5 years from 2004.
2016 is 12 years from 2004.

graphically, the equation looks like this:

$$$

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