Question

9
michael graduates from college as an engineer and receives two job offers. company a provides him a table that shows the relationship between what his salary will be each year he works at the company. create an equation that represents the relationship between his salary and years worked at company a. define your variables.
$s = 70,000 + 2,250y$
part b - company b tells michael that his starting salary in year 0 will be $60,000 and he will receive a $5,000 raise each year. michael plans to stay at the company he works at for at least 8 years. at which company will he make more money at in year 8 and by how much? justify your answer.
(table on left: years worked | salary; 0 | $70,000; 1 | $72,250; 2 | $74,500; 3 | $76,750; 4 | $79,000)

Explanation:

Step1: Define Variables for Company A

Let \( y \) be the years worked, \( S_A \) be salary at Company A. From the table, starting salary (\( y = 0 \)) is $70,000, and the raise per year: \( 72250 - 70000 = 2250 \), \( 74500 - 72250 = 2250 \), etc. So equation: \( S_A = 70000 + 2250y \).

Step2: Calculate Salary at Company A in Year 8

Substitute \( y = 8 \) into \( S_A \):
\( S_A = 70000 + 2250(8) = 70000 + 18000 = 88000 \).

Step3: Define Equation for Company B

Let \( S_B \) be salary at Company B. Starting salary (\( y = 0 \)) is $60,000, raise per year is $5,000. So equation: \( S_B = 60000 + 5000y \).

Step4: Calculate Salary at Company B in Year 8

Substitute \( y = 8 \) into \( S_B \):
\( S_B = 60000 + 5000(8) = 60000 + 40000 = 100000 \).

Step5: Compare Salaries and Find Difference

Compare \( S_A = 88000 \) and \( S_B = 100000 \). \( S_B > S_A \). Difference: \( 100000 - 88000 = 12000 \).

Answer:

In Year 8, Michael will make more money at Company B, by $12,000.