The hourly wage of of workers was raised once a year and grew exponentially from $8.508.50 to $10.8810.88 in 10 years. What was the growth rate?

The growth rate was 

The formula to calculate exponential growth is given by:

\[
A = P(1 + r)^t
\]

Where:
- $ A $ is the final amount (new wage),
- $ P $ is the initial amount (initial wage),
- $ r $ is the growth rate (as a decimal),
- $ t $ is the time in years.

In this case:
- $ A = 10.88 $,
- $ P = 8.50 $,
- $ t = 10 $ years.

Now, substitute the values into the formula:

\[
10.88 = 8.50(1 + r)^{10}
\]

To solve for $ r $, follow these steps:

1. Divide both sides by 8.50:

\[
\frac{10.88}{8.50} = (1 + r)^{10}
\]

2. Simplify:

\[
1.28 = (1 + r)^{10}
\]

3. Take the 10th root of both sides:

\[
1 + r = \sqrt[10]{1.28}
\]

4. Subtract 1 to isolate $ r $:

\[
r = \sqrt[10]{1.28} - 1
\]

Let's calculate the value of $ r $.The growth rate is approximately 0.02499, or 2.5% per year.

Would you like more details on this solution or further clarification?

Here are five related questions to consider:
1. What is the wage after 15 years if the same growth rate continues?
2. How would you calculate the time it takes for the wage to double at this growth rate?
3. How does the exponential growth model compare to linear wage growth?
4. Can you apply this growth rate to other financial situations like savings or investments?
5. What happens to the wage if the growth rate is increased to 3%?

**Tip:** When working with exponential growth, small changes in the growth rate can have a large impact over time!

The hourly wage of workers was raised once a year and grew exponentially from $8.50 to $10.88 in 10 years. What was the growth rate?

Discover how to calculate the exponential growth rate of an hourly wage that increased from $8.50 to $10.88 over 10 years. Learn the step-by-step process using the exponential growth formula A = P(1 + r)^t, suitable for students in Grades 9-12.

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