Question

In 1938, the minimum wage in the United States was 0.25 dollars. By 2009 , the minimum wage had increased to 7.25 dollars. Find the average rate of change in the minimum wage from 1938 to 2009.

Answer 1

The average rate of change in the minimum wage from 1938 to 2009 is
`\( (7 - 0.25)/(2009 - 1938) \)` dollars per year.

Step-by-step explanation:

To determine the average rate of change in the minimum wage over the specified period, we employ the formula:

`\[ \text{Average Rate of Change} = \frac{\text{Change in Quantity}}{\text{Change in Time}} \]`

In this context, the "Change in Quantity" is the difference in minimum wage values between 2009 and 1938, which equals
`\(7 - 0.25 = 6.75\)` dollars. The "Change in Time" corresponds to the difference in years, computed as
`\(2009 - 1938 = 71\)` years.

Plugging these values into the formula:

`\[ \text{Average Rate of Change} = (6.75)/(71) \]`

Upon calculation, this expression yields the average rate of change in the minimum wage per year over the period in question.

This average rate of change represents the annualized increase in the minimum wage from 1938 to 2009. It offers a simplified but informative view of the overall growth in the minimum wage during these seven decades. However, it is essential to acknowledge that this calculation assumes a linear progression, not accounting for potential variations in the rate of change over the years.