Let's carefully break down the problem to determine the correct function Sam could use to figure out his total earnings, [tex]\( E \)[/tex], for the day based on the number of people he serves, [tex]\( n \)[/tex].
1. Hourly Wage Calculation:
- Sam earns [tex]$6 per hour.
- He works for 4 hours in total.
Therefore, his earnings from the hourly wage alone can be calculated as:
\[
\text{Earnings from wage} = 6 \, (\text{dollars/hour}) \times 4 \, (\text{hours}) = 24 \, \text{dollars}
\]
2. Tips Calculation:
- Sam earns about $[/tex]2.50 in tips for each person he serves.
- Let [tex]\( n \)[/tex] be the number of people he serves.
Therefore, his earnings from tips can be expressed as:
[tex]\[
\text{Earnings from tips} = 2.5 \, (\text{dollars/person}) \times n \, (\text{number of people}) = 2.5n \, \text{dollars}
\][/tex]
3. Total Earnings Calculation:
- Sam's total earnings for the day will be the sum of his hourly wage earnings and his tips.
Combining both parts, the total earnings function [tex]\( E(n) \)[/tex] is:
[tex]\[
E(n) = \text{Earnings from wage} + \text{Earnings from tips} = 24 + 2.5n
\][/tex]
Therefore, the correct function that represents Sam's total earnings [tex]\( E \)[/tex] for the day, based on the number of people [tex]\( n \)[/tex] he serves, is:
[tex]\[
E(n) = 2.5n + 24
\][/tex]
Hence, the correct answer is:
C. [tex]\( E(n) = 2.5n + 24 \)[/tex]
