The annual salary for a manager at a company is modeled by the function ƒ(x) = 50,000(1.065)x, where x is the number of years employed. What does 1.065 represent?

Question

Responses
A The salary increases at a rate of 0.065% each year.The salary increases at a rate of 0.065% each year.
B The salary increases at a rate of 0.65% each year.The salary increases at a rate of 0.65% each year.
C The salary increases at a rate of 6.5% each year.The salary increases at a rate of 6.5% each year.
D The salary increases at a rate of 106.5% each year.

Answer 1

The function given is \( f(x) = 50,000(1.065)^x \), where \( x \) is the number of years employed. The term \( 1.065 \) represents the growth factor of the salary each year.

To understand what this means in terms of percentage increase, you can subtract 1 from this growth factor:

\[ 1.065 - 1 = 0.065 \]

To express this as a percentage, you multiply by 100:

\[ 0.065 \times 100 = 6.5% \]

Thus, the 1.065 indicates that the salary increases at a rate of 6.5% each year.

The correct answer is:

C The salary increases at a rate of 6.5% each year.