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.

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.