Year of Experience Salary

Question

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.The rate of change per year is the same for Company A and Company B.

Answer 1

To determine the rate of change for both Company A and Company B, we can analyze the data provided.

For Company A:

• From the provided data:
  • The increases in salary for the years worked are:
    • From Year 1 to Year 2: $33,450 - $33,300 = $150
    • From Year 2 to Year 4: $33,750 - $33,450 = $300
    • From Year 4 to Year 6: $34,050 - $33,750 = $300
• The increments are not uniform, so we check the average increase over the total period:
  • Total increase from Year 1 to Year 6: $34,050 - $33,300 = $750
  • Number of years between 1 and 6 is 5 years, resulting in an average rate of change:
    • Average rate of change = Total increase / Number of years = $750 / 5 = $150 per year.

For Company B:

• The linear function given is y = 200x + $29,000. The coefficient of x (200) represents the rate of change (or salary increase per year).
• Thus, the rate of change for Company B is $200 per year.

Now, comparing the rates of change:

• Company A has a rate of change of $150 per year.
• Company B has a rate of change of $200 per year.

The difference is:

• Company B’s rate of change ($200) - Company A’s rate of change ($150) = $50.

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