To determine which function accurately represents Sam’s total earnings [tex]\( E \)[/tex] for a day, we need to consider both his hourly wage and the tips he earns per person served.
### Step-by-Step Calculation:
1. Calculate Sam’s earnings from his hourly wage:
- Sam earns \[tex]$6 per hour.
- He works for 4 hours.
\[
\text{Earnings from hours} = 6 \, \text{dollars/hour} \times 4 \, \text{hours} = 24 \, \text{dollars}
\]
2. Calculate Sam’s earnings from tips:
- Sam earns \$[/tex]2.50 per person he serves.
- Let [tex]\( n \)[/tex] be the number of people served.
[tex]\[
\text{Earnings from tips} = 2.5 \, \text{dollars/person} \times n \, \text{persons} = 2.5n \, \text{dollars}
\][/tex]
3. Determine the total earnings [tex]\( E \)[/tex]:
- Total earnings [tex]\( E \)[/tex] is the sum of his earnings from his hourly wage and from tips.
[tex]\[
E(n) = \text{Earnings from hours} + \text{Earnings from tips}
\][/tex]
Substituting the values:
[tex]\[
E(n) = 24 + 2.5n
\][/tex]
Given the choices provided, the function that Sam can use to figure out his total earnings for the day is:
C. [tex]\( E(n) = 2.5n + 24 \)[/tex]
This matches the derived function based on Sam's hourly wage and tips per person served.
