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.