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AlgebraQ&A LibraryA pair of women's running shoes cost $110 in 2005 and the same shoes cost $120 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. a. 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.) b. The estimated price of the running shoes in 2015 will be $__.(Round to two decimal places as needed.)Question

Asked Feb 7, 2020

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A pair of women's running shoes cost $110 in 2005 and the same shoes cost $120 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.

a. 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.)

b. The estimated price of the running shoes in 2015 will be $__.

(Round to two decimal places as needed.)

Step 1

It is given that the pair of woman running shoes costs $110 in 2005 and the same shoes cost $120 in 2009 due to inflation.

And, the given exponential model is

Step 2

To find:

- The exponential model over the time period 2005 to 2009.
- Using, model in part (a) estimate the price of shoes in 2015, if the inflation continuous at the same rate.

Step 3

- Since at x=0 in 2005, the cost of shoes is $110 and the same shoes cost $120 in 2009 at x=4.

Therefore, from (1), satisfying x=4 and plugging y=120.

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