Question

Mark just landed a great job as an engineer where he will make $65,000 a year. The company he will work for guarantees a 2% pay increase each year so its employees' salaries keep up with inflation. At the end of the 1st year, Mark will have made $65,000 dollars. What is the explicit function that represents Mark's salary at the end of his second year?

A. S(t) = 65,000 + 0.02t
B. S(t) = 65,000(1.02)^t
C. S(t) = 65,000 + 1.02t
D. S(t) = 65,000 + 0.02

Answer 1

The explicit function that represents Mark's salary at the end of his second year, after a yearly 2% increase, is option B: S(t) = 65,000(1.02)^t.

The correct option is B.

Step-by-step explanation:

The student's question is about finding the explicit function that represents Mark's salary at the end of his second year, given that he has a guaranteed 2% pay increase each year. To calculate the salary at the end of the second year, we use the formula that accounts for a percentage increase compounded annually.

The correct formula for this situation is S(t) = 65,000(1.02)^t, where t is the number of years. This means that after 1 year, his salary will be 65,000 multiplied by 1.02 (which is the original amount plus a 2% increase). Therefore, the explicit function that fits this scenario is option B. S(t) = 65,000(1.02)^t.

The correct option is B.