To determine which museum's entrance fee is proportional to the number of visitors, we need to check if the ratio of the fee to the number of visitors is constant for each museum. Let's examine each museum one by one.
Museum A:
- For 2 visitors, the fee is \[tex]$4. The ratio is \( \frac{4}{2} = 2 \).
- For 3 visitors, the fee is \$[/tex]5. The ratio is [tex]\( \frac{5}{3} \approx 1.67 \)[/tex].
- For 4 visitors, the fee is \[tex]$6. The ratio is \( \frac{6}{4} = 1.5 \).
Since the ratio of fee per visitor is not constant (2, 1.67, 1.5), the entrance fee at Museum A is not proportional to the number of visitors.
Museum B:
- For 1 visitor, the fee is \$[/tex]2. The ratio is [tex]\( \frac{2}{1} = 2 \)[/tex].
- For 4 visitors, the fee is \[tex]$8. The ratio is \( \frac{8}{4} = 2 \).
- For 6 visitors, the fee is \$[/tex]11. The ratio is [tex]\( \frac{11}{6} \approx 1.83 \)[/tex].
Since the ratio of fee per visitor is not constant (2, 2, 1.83), the entrance fee at Museum B is not proportional to the number of visitors.
Museum C:
- For 3 visitors, the fee is \[tex]$4. The ratio is \( \frac{4}{3} \approx 1.33 \).
- For 12 visitors, the fee is \$[/tex]16. The ratio is [tex]\( \frac{16}{12} = \frac{4}{3} \approx 1.33 \)[/tex].
- For 18 visitors, the fee is \$24. The ratio is [tex]\( \frac{24}{18} = \frac{4}{3} \approx 1.33 \)[/tex].
Since the ratio of fee per visitor is constant ([tex]\(\frac{4}{3}\)[/tex]), the entrance fee at Museum C is proportional to the number of visitors.
Therefore, the correct answer is:
C. museum C
