Question
Heather just got hired as an administrative assistant at Haven Enterprises. Her starting salary is $45,500, and her contract ensures that she will get a 3% salary increase each year.
Write an exponential equation in the form y=a(b)^x that can model Heather's salary, y, after x years.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Write an exponential equation in the form y=a(b)^x that can model Heather's salary, y, after x years.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Answers
GPT-4o mini
To write an exponential equation that models Heather's salary after x years, we can start with her initial salary and the annual percentage increase.
1. Her starting salary (a) is $45,500.
2. The growth factor (b) can be determined from the salary increase. Since she gets a 3% increase each year, her salary after each year is multiplied by (1 + 0.03) = 1.03.
Thus, we can express her salary after x years with the following equation:
\[
y = 45500 \times (1.03)^x
\]
Here:
- \(y\) is her salary after \(x\) years,
- \(a = 45500\) (the initial salary),
- \(b = 1.03\) (the growth factor due to the salary increase),
- \(x\) is the number of years.
So, the final exponential equation that models Heather's salary after x years is:
\[
y = 45500 \times (1.03)^x
\]
1. Her starting salary (a) is $45,500.
2. The growth factor (b) can be determined from the salary increase. Since she gets a 3% increase each year, her salary after each year is multiplied by (1 + 0.03) = 1.03.
Thus, we can express her salary after x years with the following equation:
\[
y = 45500 \times (1.03)^x
\]
Here:
- \(y\) is her salary after \(x\) years,
- \(a = 45500\) (the initial salary),
- \(b = 1.03\) (the growth factor due to the salary increase),
- \(x\) is the number of years.
So, the final exponential equation that models Heather's salary after x years is:
\[
y = 45500 \times (1.03)^x
\]