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A pair of women's shoes cost $115 in 2004 and the same shoes cost $140 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 2015. y = 115 ( _____) ^x [round to four decimal places as needed]

Respuesta :

The rate of inflation can be modeled by the following equation:

[tex]y\text{ = 115}\times(A)^x^{}[/tex]

We have to find A to solve letter a). The exercise gives the information that in 5 years (2004-2009) the price went to $140 (this is the 'y' value of the formula). Therefore:

[tex]140\text{ = 115}\times A^5[/tex][tex]A\text{ = }\sqrt[5]{\frac{140}{115}}=1.0401[/tex]

So the exponential model is going to be:

[tex]y\text{ = 115}\times(1.0401)^x[/tex]

To solve letter b, we have now 11 years (2004-2015) and the objective is to find the 'y' value:

[tex]y\text{ = 115}\times(1.0401)^{11}=177.22\text{ dollars}[/tex]

So the answers will be:

[tex]a)\text{ y = 115}\times(1.0401)^x[/tex][tex]b)\text{ \$177}.22[/tex]

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