calculus project
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Calculus Project
By: Stacie Burke
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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.
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a) Use a trapezoid Riemann sum to find how many students go through the lunch line from 0 to 30 minutes.
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Solution:a)
f(t) dt =
5(0 + 2(35) + 2(50) + 2(42) + 2(17) + 4) 2
= 868 students
0
30
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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.
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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.
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b) 1 f(t) dt = 1 868 = 30 30
29 students per minute
0
30
Solution:
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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.
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c) Find the acceleration of the lunch line from 5 to 10 minutes.
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c) f(10) – f(5) = 50 - 35 = 3 10 – 5 5
3 students per squared minute
Solution:
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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.