Question

Year of Experience Salary
1 $33,300
2 $33,450
4 $33,750
6 $34,050


The table shows the salary of an employee after x years of working for Company A. The linear function y = 200x + $29,000 represents the salary, y, of an employee in the same position working at Company B for x number of years. Which statement BEST compares the rate of change per year for the employee at Company A and the employee at Company B?
Responses
A The rate of change per year for Company A's employee is $50 less than Company B's rate of change per year.The rate of change per year for Company A's employee is $50 less than Company B's rate of change per year.
B The rate of change per year for Company A's employee is $150 greater than Company B's rate of change per year.The rate of change per year for Company A's employee is $150 greater than Company B's rate of change per year.
C The rate of change per year for Company B's employee is $200 greater than Company A's rate of change per year.The rate of change per year for Company B's employee is $200 greater than Company A's rate of change per year.
D The rate of change per year is the same for Company A and Company B.

Answer 1

To compare the rate of change in salary for both Company A and Company B, we need to determine the rate of change from the data provided.

**Company A:**
We have the following salary data over the years:
- Year 1: $33,300
- Year 2: $33,450
- Year 4: $33,750
- Year 6: $34,050

We'll calculate the rate of change for Company A from the given data.

1. From year 1 to year 2:
- Change in salary = $33,450 - $33,300 = $150
- Change in years = 2 - 1 = 1 year
- Rate of change = $150 / 1 = $150 per year

2. From year 2 to year 4:
- Change in salary = $33,750 - $33,450 = $300
- Change in years = 4 - 2 = 2 years
- Rate of change = $300 / 2 = $150 per year

3. From year 4 to year 6:
- Change in salary = $34,050 - $33,750 = $300
- Change in years = 6 - 4 = 2 years
- Rate of change = $300 / 2 = $150 per year

The rate of change for Company A consistently appears to be $150 per year.

**Company B:**
The linear function for Company B's salary is given as:
\[ y = 200x + 29,000 \]

The coefficient of \( x \) (200) represents the rate of change in salary per year. Therefore, the rate of change for Company B is $200 per year.

**Comparison:**
- Company A's rate of change: $150 per year
- Company B's rate of change: $200 per year

To compare these:
- The difference in rates of change = $200 - $150 = $50

Thus, the rate of change per year for Company A's employee is $50 less than Company B's rate of change per year.

**Final Answer:**
A. The rate of change per year for Company A's employee is $50 less than Company B's rate of change per year.