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WIR Math 131-copyright Joe Kahlig, 07a
Week in Review # 7
Sections 5.1
Things to know:
• Be able to compute a left sum or right sum for a data set.
• Be able to estimate total change using a graph.
1. Filters at a water treatment plant become less effective over time and hence the amount
of pollution passing through the filters increases over time. The rate that pollution
passes through the filters is given by the table.
Day
rate (kg/day)
0
3
7 14 21
5 8 15
28 35
25 45
(a) Estimate the amount of pollution passing through the filters during the 35 days
using the following methods.
i. left sum
ii. right sum
iii. average of the two previous results.
(b) Which of the estimates is a lower estimate? upper estimate?
2. The function graphed is the speed (meters/minute) of somebody ridding a bike. Give
the total distance traveled during that 40 minutes.
meter/min
40
30
20
10
5
10
15
20
25
30
35 40
minutes
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WIR Math 131-copyright Joe Kahlig, 07a
3. The graph shows the velocity of an object in meters/sec. Estimate the distance traveled between t = 0 and t = 6 using the methods listed below.
(a) left sum with 3 rectangles
meter/sec
25
20
15
10
5
1
2
3
4
5
6
7
8
sec
(b) right sum with 3 rectangles
meter/sec
25
20
15
10
5
1
2
3
4
5
6
7
8
sec
(c) right sum with 6 rectables
meter/sec
25
20
15
10
5
1
2
3
4
5
6
7
8
sec
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WIR Math 131-copyright Joe Kahlig, 07a
(d) by counting rectangles.
meter/sec
25
20
15
10
5
1
2
3
4
5
6
7
8
sec
4. The graph shows the velocity of an object in mph. Estimate the distance traveled
between t = 0 and t = 8 by counting rectangles
mph
8
6
4
2
1
2
3
4
5
6
7
8
hour