Math Problem Statement
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
Solution
The formula to calculate exponential growth is given by:
Where:
- is the final amount (new wage),
- is the initial amount (initial wage),
- is the growth rate (as a decimal),
- is the time in years.
In this case:
- ,
- ,
- years.
Now, substitute the values into the formula:
To solve for , follow these steps:
- Divide both sides by 8.50:
- Simplify:
- Take the 10th root of both sides:
- Subtract 1 to isolate :
Let's calculate the value of .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:
- What is the wage after 15 years if the same growth rate continues?
- How would you calculate the time it takes for the wage to double at this growth rate?
- How does the exponential growth model compare to linear wage growth?
- Can you apply this growth rate to other financial situations like savings or investments?
- 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!
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Math Problem Analysis
Mathematical Concepts
Exponential Growth
Algebra
Formulas
A = P(1 + r)^t
r = (A / P)^(1/t) - 1
Theorems
Exponential Growth Formula
Suitable Grade Level
Grades 9-12
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