Suppose you make $10 an hour at your job that you have been working at for 5 years. Each year, you get a 6% raise.
1. Write an equation that models this situation.
Is this correct?
y=10(1.06)^x
Yes, you are correct! The equation y = 10(1.06)^x models the situation accurately. Allow me to explain how we arrived at this equation:
In this situation, we start with an initial hourly wage of $10 and receive a 6% raise each year. To represent this recurring increase, we multiply the previous year's wage by 1.06 (which represents the 6% raise) for every subsequent year.
Breaking down the equation:
- The variable y represents the hourly wage at a particular year.
- The base value 10 represents the initial hourly wage.
- The term (1.06)^x represents the compounding effect of the 6% raise each year, where x is the number of years since the beginning of employment.
For example, if you want to find the hourly wage after 5 years, you would substitute x = 5 into the equation:
y = 10(1.06)^5
y = 10(1.3382)
y ≈ $13.38
So after 5 years, the hourly wage would be approximately $13.38.