Question

lesson 3 cool down
an art museum opens at 9 a.m. and closes at 5 p.m. the function v gives the number of
visitors in a museum h hours after it opens.

1. explain what this statement tells us about the situation: v(1.25) = 28.
2. use function notation to represent each statement:

a. at 1 p.m., there were 257 visitors in the museum.
b. at the time of closing, there were no visitors in the museum.

Explanation:

Question 1

The function \( V(h) \) gives the number of visitors \( h \) hours after the museum opens (at 9 a.m.). For \( V(1.25) = 28 \), \( h = 1.25 \) hours means 1 hour and 15 minutes (since \( 0.25\times60 = 15 \) minutes) after 9 a.m. So, 1.25 hours after 9 a.m. (which is 10:15 a.m.), the number of visitors in the museum is 28.

The museum opens at 9 a.m. At 1 p.m., the number of hours since opening is \( 13 - 9 = 4 \) hours (since 1 p.m. is 13:00 in 24 - hour time). The function \( V(h) \) represents the number of visitors \( h \) hours after opening, and there are 257 visitors. So we use function notation \( V(4)=257 \).

The museum closes at 5 p.m. The number of hours from 9 a.m. to 5 p.m. is \( 17 - 9 = 8 \) hours. At closing time, there are no visitors, so the number of visitors \( V \) at \( h = 8 \) hours (when the museum closes) is 0. So we write \( V(8)=0 \).

Answer:

1.25 hours after the museum opens (at 10:15 a.m.), there are 28 visitors in the museum.

Question 2a