Question

A pair of women's shoes cost $110 in 2008 and the same cost $120 in 2013 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 from (a) to estimate the price of shoes in 2018. the rate of inflation can be modeled by the following exponential equation, where the model solves for the inflated price y after time x.
`y = 110( \: \: \: \: \: ) ^(x)`round to four decimal places as needed.

Answer 1

Okay, here we have this:

Considering the model we obtain the following:

`\begin{gathered} t=2013-2008=5 \\ 120=110(1-z)^5 \\ z=\sqrt[5]{(12)/(11)-1} \\ z\approx0.0176 \end{gathered}`

Here we obtain that the model that describes the rate of inflation is:

`\begin{gathered} y=110(1+0.0176)^x \\ y=110(1.0176)^x \end{gathered}`

b) In this case we obtain:

`\begin{gathered} x=2018-2008=10 \\ y=110\mleft(1.0176\mright)^(10) \\ y=130.9675 \end{gathered}`