Question

the following table shows buying power of a worker earning the federal minimum wage for various years. this is not the actual minimum wage but the minimum wage adjusted for inflation. for instance, the actual minimum wage in 1970 was $1.60. spending $1.60 in 1970 was the same as spending $6.95 in 2005.

(a) what was the average annual rate of change in the inflation - adjusted minimum wage from 1995 to 2005? (note: a negative average rate of change denotes a decrease.)(round to the nearest hundredth of a cent.)

(b) prior to 1990, in which five - year period did the average annual rate of change in the inflation - adjusted minimum wage increase?

what was the average annual rate of change during that period?

Explanation:

Step1: Calculate the time difference

The time period from 1995 to 2005 is \(2005 - 1995=10\) years.

Step2: Calculate the change in wage

The adjusted minimum wage in 1995 is \(5.40\) and in 2005 is \(5.15\). The change in wage is \(5.15 - 5.40=- 0.25\) dollars. Since \(1\) dollar \( = 100\) cents, the change is \(-0.25\times100=-25\) cents.

Step3: Calculate the average annual rate of change

The formula for the average rate of change is \(\frac{\text{Change in quantity}}{\text{Change in time}}\). So the average annual rate of change is \(\frac{-25}{10}=-2.50\) cents per year.

Answer:

-2.50 cents per year