Exponential Decay: More Bounce to the Ounce
Name ______________________________________
Pollution and Cleanup of an Aquarium Experiment:
Clean water: ____________
Oil: ______________
Cleanup Stage
Amount of Oil
0
20
1
2
3
4
5
6
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8
9
10
Cleanup Stage
Amount of Oil
11
12
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14
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20
21
20
y
a. Describe the pattern of change in your graph.
18
16
14
b. Use your calculator to find a regression model that best fits
your data.
12
10
8
6
4
2
2
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20
x
1. Suppose a new golf ball drops downward from a height of 27 feet onto a paved parking lot and keeps
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bouncing up and down, again and again. Rebound height of the ball should be of its drop height. Make a
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table and plot the data showing expected heights of the first ten bounces of the golf ball.
Bounce Number 0
1
2
3
4
5
6
7
8
9
10
Rebound Height
27
(in feet)
30
y
a. How does the rebound height change from one bounce
to the next? How does the shape of the data plot show
that pattern?
27
24
21
18
b. Write a now-next rule to describe the height of a
bounce after the previous one.
15
12
9
6
3
1
2
3
4
5
6
7
8
9
10
x
c. Write a “y = …” rule to calculate the rebound height y at
any stage x.
d. How will the data table, plot, and rules for calculating rebound height change if the ball only drops from
15 feet?
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2. When dropped onto a hard surface, a brand new softball should rebound to about 5 the height from
which it is dropped. A brand new softball is dropped 25 feet from a window onto concrete. Make a table
and plot the data showing expected heights of the first 5 bounces of the softball.
Bounce Number
Rebound Height (in feet)
0
25
1
2
3
4
5
a. Write a now-next rule to describe the
height of one bounce after the previous
one.
y
25
20
15
10
b. Write a “y = …” rule to calculate the
rebound height y for any stage x.
5
1
2
3
4
5
x
c. How will the data table, plot, and rules for calculating rebound height change if the ball only drops
from 15 feet?
3. Here are some data from bounce tests of a softball dropped from a height of 10 feet.
Bounce Number
1
2
3
4
Rebound Height (in feet) 3.8
1.3
0.6
0.2
a. What do these data tell you about the quality of the tested softball?
b. Use your calculator to find the exponential model that best fits the data.
c. What do the numbers from your model tell you about the situation?
5
0.05