There are 700 people in line for a popular amusement-park ride when the ride begins operation...

  

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There are 700 people in line for a popular amusement-park ride when the ride begins operation in the morning. Once it begins operation, the ride accepts passengers until the park closes 8 hours later. While there is a line, people move onto the ride at a rate of 800 people per hour. The graph shows the rate, r(t), at which people arrive at the rate throughout the day. Time is measured in hours from the time the ride begins operation. a. How many people arrive at the ride between t = 0 and t = 3? Show work. b. Is the number of people waiting to get on the ride increasing or decreasing between t = 2 and t = 3? Justify your answer. People per Hour 1,400- 1,200- 1,000- 800 600- 400- 200- 04 0 Time (hours) c. At what time is the line for the ride the longest? How many people are in line at that time? Justify your answers. d. Write, but do not solve, an equation involving an integral expression of r whose solutions gives the earliest time t at which there is no longer a line for the ride. There are 700 people in line for a popular amusement-park ride when the ride begins operation in the morning. Once it begins operation, the ride accepts passengers until the park closes 8 hours later. While there is a line, people move onto the ride at a rate of 800 people per hour. The graph shows the rate, r(t), at which people arrive at the rate throughout the day. Time is measured in hours from the time the ride begins operation. a. How many people arrive at the ride between t = 0 and t = 3? Show work. b. Is the number of people waiting to get on the ride increasing or decreasing between t = 2 and t = 3? Justify your answer. People per Hour 1,400- 1,200- 1,000- 800 600- 400- 200- 04 0 Time (hours) c. At what time is the line for the ride the longest? How many people are in line at that time? Justify your answers. d. Write, but do not solve, an equation involving an integral expression of r whose solutions gives the earliest time t at which there is no longer a line for the ride.