Question

question
grace was offered a job after college earning a salary of $30,000. she will get a raise of $2,000 after each year working for the company. answer the questions about 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, an
dependent variable is the, because the
depends on the.
a function relating these variables is c(x) =
so c(4) =, meaning 4

Explanation:

Step1: Identify variables

The independent variable \( x \) represents the number of years working (since it's the variable we can control or that changes independently). The dependent variable is the salary (since it depends on the number of years worked).

Step2: Formulate the function

The initial salary is $30,000, and each year (each LXI0) there's a raise of $2,000. So this is a linear function. The general form of a linear function is \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y-intercept (initial value). Here, \( m = 2000 \) (raise per year) and \( b = 30000 \) (initial salary). So the function \( C(x) \) (salary as a function of years \( x \)) is \( C(x)=2000x + 30000 \).

Step3: Calculate \( C(4) \)

Substitute \( x = 4 \) into the function: \( C(4)=2000(4)+30000 \). First, calculate \( 2000\times4 = 8000 \). Then add 30000: \( 8000 + 30000 = 38000 \). This means after 4 years of working, the salary is $38,000.

Answer:

• The independent variable \( x \) represents the number of years working, and the dependent variable is the salary, because the salary depends on the number of years working.
• A function relating these variables is \( C(x)=\boldsymbol{2000x + 30000} \).
• So \( C(4)=\boldsymbol{38000} \), meaning 4 years after working at the company, Grace's salary is $38,000.