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

To find the price of a haircut in 2008, multiply the initial price by the inflation factor. The cost of a haircut in 2013 can be found using the same method.

Step-by-step explanation:

To find the price of a haircut in 2008, we first need to calculate the percentage increase in prices from 1998 to 2008. The total inflation rate during this period is 51%. Now, let's calculate the new price of the haircut using the inflation rate.

Step 1: Calculate the inflation factor: 1 + (Inflation rate / 100) = 1 + (51 / 100) = 1.51

Step 2: Multiply the original price of the haircut in 1998 by the inflation factor: $18 * 1.51 = $27.18

Therefore, the price of a haircut at the salon in 2008 would be $27.18.

To find the cost of a basic haircut in 2013, we can use the same method. Given that the price was $19.95 in 2003, we need to find the new price in 2013 using the inflation factor:

Step 1: Calculate the inflation factor: 1 + (Inflation rate / 100) = 1 + (51 / 100) = 1.51

Step 2: Multiply the price in 2003 by the inflation factor: $19.95 * 1.51 = $30.15

Therefore, the cost of a basic haircut in 2013 would be $30.15.

Answer 2

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