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.)

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.)
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Expert Answer

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

Algebra homework question answer, step 1, image 1

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.

Algebra homework question answer, step 3, image 1

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Algebra