Question

Autumn was offered a job after college earning a salary of $55,000. She will get a raise of $4,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company.
Answer
Attempt 1 out of 2

The independent variable, x, represents the
number of years worked
, and the dependent variable is the
salary
, because the
salary
depends on the
number of years worked
.
A function relating these variables is H, of, x, equalsH(x)=
.
So H, of, 8, equalsH(8)=
, meaning 88


.

Answer 1

Let's define the function relating the salary to the number of years worked at the company.

1. **Independent and Dependent Variables**:
- The independent variable, \( x \), represents the **number of years worked**.
- The dependent variable \( H(x) \) represents the **salary**, because the salary depends on the number of years worked.

2. **Function Definition**:
Autumn's starting salary is $55,000, and she receives a raise of $4,000 every year. We can establish the function as follows:

\[
H(x) = 55000 + 4000x
\]

This function indicates that for each year \( x \), her salary increases by $4,000.

3. **Calculating Salary for 8 Years**:
To find \( H(8) \):

\[
H(8) = 55000 + 4000(8)
\]
\[
H(8) = 55000 + 32000
\]
\[
H(8) = 87000
\]

So \( H(8) = 87000 \).

In summary, the function relating the salary to the number of years worked is:

\[
H(x) = 55000 + 4000x
\]

And \( H(8) = 87000 \), meaning after 8 years, Autumn's salary will be $87,000.