Applying Riemann sums to rates of change in general. A concert is being held in
ID: 3147954 • Letter: A
Question
Applying Riemann sums to rates of change in general. A concert is being held in the Fine Arts building auditorium. The rate at which people enter (in people per minute) is measured, and the measurements produce the following graph: Please explain your process 50 35 30 15 10 lsc 12 18 20 Time (minutes) Assuming nobody leaves the auditorium over this 20-minute period, and assuming the auditorium was empty at the beginning, approximately how many people are in the auditorium at the end of the 20 minutes?Explanation / Answer
We simply need to find the area under the curve.
We can do this by breaking this curve into different trapeziums and find the area separately for every minute and then can add it to get the final answer.
From 0 - 2 minute: 0.5 ( 15 + 30 ) * 2 = 45 people.
From 2 - 4 minute: 0.5 ( 30+ 37 ) * 2 = 67 people.
From 4 - 6 minute: 0.5 ( 37 + 40 ) * 2 = 87 people.
From 6 - 8 minute: 0.5 ( 40 + 30 ) * 2 = 70 people.
From 8 - 10 minute: 0.5 ( 30 + 20 ) * 2 = 50 people.
From 10 - 14 minute: 0.5 ( 20 + 10 ) * 4 = 60 people.
From 14 - 18 minute: 0.5 ( 10 + 5 ) * 4 = 30 people.
From 18 - 20 minute: 0.5 ( 5 + 0 ) * 2 = 10 people.
Adding all the above values, we get 419 people.
Since no one left in the mean time, we can say that approximately 419 people are there in the auditorium at the end of the 20 minutes.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.