Question

The hourly wage of workers was raised once a year and grew exponentially from 9.00 to12.10 in 10 years. What was the growth rate?

Answer 1

The growth rate of the workers' hourly wage that increased from $9.00 to $12.10 over 10 years is approximately 3.03%, calculated using the formula for exponential growth and solving for the growth rate.

Step-by-step explanation:

To calculate the growth rate of the workers' hourly wage over 10 years, we can use the formula for exponential growth, which is final amount = initial amount * (1 + growth rate)^number of periods. In this case, the final amount is $12.10, the initial amount is $9.00, and the number of periods is 10 years. We can then rearrange the formula to solve for the growth rate:

12.10 = 9.00 * (1 + growth rate)^10

Dividing both sides by 9.00, we get:

(12.10 / 9.00) = (1 + growth rate)^10

Now we take the 10th root of both sides to solve for 1 + growth rate and then subtract 1 to find the growth rate. By using a calculator, we would find that the growth rate is approximately 0.0303 or 3.03%

This is a percent increase from the initial wage to the final wage over the course of a decade, taking into account the compounding effect of the yearly raise.