High School

A consultant charges her clients for her services based on an equation relating the total bill [tex]f(h)[/tex] to the number of hours worked [tex]h[/tex]. The best interpretation of this function [tex]f(h) = 125h + 150[/tex] is:

A. She charges [tex]\$150[/tex] per hour plus a [tex]\$125[/tex] flat fee.
B. She charges [tex]\$125[/tex] per hour plus a [tex]\$150[/tex] flat fee.
C. She charges [tex]\$275[/tex] per hour.
D. Her hourly charges vary from [tex]\$125[/tex] to [tex]\$150[/tex] depending on the job.

Answer :

We are given the function

[tex]$$
f(h) = 125h + 150,
$$[/tex]

where [tex]$h$[/tex] represents the number of hours worked.

Step 1: Identify the hourly charge.
The term [tex]$125h$[/tex] indicates that for each hour worked, the consultant charges \[tex]$125. This is because the coefficient of $[/tex]h[tex]$, which is 125, represents the rate per hour.

Step 2: Identify the flat fee.
The constant term $[/tex]150[tex]$ is independent of the number of hours worked. This tells us that regardless of how many hours are worked, there is always a flat fee of \$[/tex]150 added to the total bill.

Step 3: Combine the results.
Thus, the function means that the total bill is calculated by adding a flat fee of \[tex]$150 to the charge of \$[/tex]125 per hour.

Therefore, the correct interpretation is that the consultant charges \[tex]$125 per hour plus a \$[/tex]150 flat fee.

The best answer is: Option B.