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Calculus Project
By: Stacie Burke
The rate at which students go through a lunch line is shown in the
following table and graph, f(t), where t is measured in minutes from 0 to
30. The rate is measured in students per minute.
a) Use a trapezoid Riemann sum to find how many students go through the lunch line from 0 to 30 minutes.
Solution:a)
f(t) dt =
5(0 + 2(35) + 2(50) + 2(42) + 2(17) + 4) 2
= 868 students
0
30
Use the 6 even segments the data is divided into. Since the area of a trapezoid is (height x (base 1 + base 2))/2 you must find the area of each trapezoid and then add them all together. This will give you
the number of students that went through the lunch line.
b) What is the average rate at which students go through the
lunch line from 0 to 30 minutes? Round to the nearest whole
number.
b) 1 f(t) dt = 1 868 = 30 30
29 students per minute
0
30
Solution:
To find the average rate you must first find the integral from 0 to 30 minutes and then divide it by 30. You divide by 30 because you are
trying to find the average and 30 is the number of minutes you have
total.
c) Find the acceleration of the lunch line from 5 to 10 minutes.
c) f(10) – f(5) = 50 - 35 = 3 10 – 5 5
3 students per squared minute
Solution:
To find the acceleration from 5 to 10 minutes take the derivative. To find
the derivative when there is no equation find the slope from 5 to 10. This will give you the acceleration in
students per squared minutes.