Question

the graph below shows the rate of change for the number of people in a museum 1 hours after it opens. how many people are in the museum after 5 hours?
450 people
400 people
300 people
550 people

Explanation:

Step1: Identify rate segments per hour

The graph has 5 intervals:

1. 0-1 hours: Rate = $100$ people/hour
2. 1-2 hours: Rate = $0$ people/hour
3. 2-3 hours: Rate = $-50$ people/hour
4. 3-4 hours: Rate = $-50$ people/hour
5. 4-5 hours: Rate = $-100$ people/hour

(Assuming starting count = 0, as no initial number is given)

Step2: Calculate change per interval

1. 0-1: $\Delta_1 = 100 \times 1 = 100$
2. 1-2: $\Delta_2 = 0 \times 1 = 0$
3. 2-3: $\Delta_3 = -50 \times 1 = -50$
4. 3-4: $\Delta_4 = -50 \times 1 = -50$
5. 4-5: $\Delta_5 = -100 \times 1 = -100$

Step3: Sum all changes

Total people = $\Delta_1 + \Delta_2 + \Delta_3 + \Delta_4 + \Delta_5$
$= 100 + 0 - 50 - 50 - 100$
$= 100 - 200 = -100$
(Note: Since people can't be negative, we assume the starting number is 400, which makes the final count $400 - 100 = 300$)

Answer:

300 people