A telemarketer earns a base salary of [tex] \$3,000 [/tex] per month, plus an annual bonus of [tex] 2.5\% [/tex] of total sales above [tex] \$250,000 [/tex]. Which function represents the annual salary for total sales of [tex] x [/tex] dollars, where [tex] x [/tex] is greater than [tex] \$250,000 [/tex]?

A. [tex] S(x) = 3,000 + 0.025(x - 250,000) [/tex]
B. [tex] S(x) = 3,000 + 2.5(x - 250,000) [/tex]
C. [tex] S(x) = 12(3,000) + 0.025(x - 250,000) [/tex]
D. [tex] S(x) = 12(3,000) + 2.5(x - 250,000) [/tex]



Answer :

To find the function that represents the annual salary for total sales of [tex]\( x \)[/tex] dollars, where [tex]\( x \)[/tex] is greater than \[tex]$250,000, we need to consider both the base salary and the additional bonus. 1. Base Salary Calculation: - The telemarketer earns a base salary of \$[/tex]3,000 per month.
- The annual base salary is calculated by multiplying the monthly salary by 12.
[tex]\[ \text{Annual Base Salary} = 12 \times 3000 = \$36,000 \][/tex]

2. Bonus Calculation:
- The telemarketer earns an annual bonus which is 2.5% of total sales above \[tex]$250,000. - To calculate the bonus, first determine the amount of sales above \$[/tex]250,000. This is given by [tex]\( x - 250,000 \)[/tex].
- The bonus is 2.5% of this amount. In decimal form, 2.5% is 0.025.
[tex]\[ \text{Bonus} = 0.025 \times (x - 250,000) \][/tex]

3. Total Annual Salary Calculation:
- The total annual salary [tex]\( S(x) \)[/tex] is the sum of the annual base salary and the bonus.
[tex]\[ S(x) = \text{Annual Base Salary} + \text{Bonus} \][/tex]
- Substituting the values we calculated:
[tex]\[ S(x) = 36,000 + 0.025 \times (x - 250,000) \][/tex]

Thus, the function representing the annual salary for total sales of [tex]\( x \)[/tex] dollars is:
[tex]\[ S(x) = 12(3,000) + 0.025(x - 250,000) \][/tex]

Therefore, the correct function is:
[tex]\[ S(x) = 12(3,000) + 0.025(x - 250,000) \][/tex]