Question

Between 1998 and 2018, inflation for prices of goods and services has been about 51%. Suppose a salon charged $18 for a basic haircut in 1998 and has been raising prices by a steady percentage each year to keep up with inflation.
What is the price of a haircut at the salon in 2008? Explain or show your reasoning.

In 2003, the salon charged $19.95 for a basic haircut. Find the cost of the basic haircut in 2013. Explain your reasoning.

Answer 1

9514 1404 393

Answer:

• $22.12
• $24.51

Step-by-step explanation:

For some growth factor f each year, the growth factor over 20 years is given as ...

  f^20 = 1 +0.51 = 1.51

Then the growth factor in 10 years is ...

  f^10 = (f^20)^(1/2) = √1.51 ≈ 1.22882

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a) In the 10 years between 1998 and 2008, the price of a basic haircut would rise to ...

  $18 × 1.22882 ≈ $22.12 . . . price in 2008

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b) In the 10 years between 2003 and 2013, the price of a basic haircut would rise to ...

  $19.95 × 1.22882 ≈ $24.51 . . . price in 2013