Advanced Mathematical Decision Making 2010 Activity Sheet 12 Answers
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Student:
Class:
Date:
Using Recursion in Models and Decision Making: Recursion in Exponential
Growth and Decay
IV.B Student Activity Sheet 3: Recursion and Exponential Functions
Different balls bounce at various heights depending on things like the type of ball, the
pressure of air in the ball, and the surface on which it is bounced. The rebound percentage
of a ball is found by determining the quotient of the rebound height (that is the height of
each bounce) to the height of the ball before that bounce, converted to a percentage.
1. Collect data on a bouncing ball that show the maximum height of at least five bounces of
the ball. Then make a scatterplot of the maximum height as a function of the bounce
number. (Let Bounce 0 be the initial drop height of the ball.)
Bounce
No.
0
Height
6
Height
62
1
31
2
15
3
8
4
4
5
1
4
2
5
Bounce
2. Find the average rebound percentage for your ball. Show your work.
Bounce
No.
0
Height
Process
Rebound
Percentage
62
1
31
31/62
50%
2
15
15/31
48.4%
3
8
8/15
53.3%
4
4
4/8
50%
5
1
1/4
25%
Charles A. Dana Center at The University of Texas at Austin
Advanced Mathematical Decision Making (2010)
Activity Sheet 3, 5 pages
10
Student:
Class:
Date:
Using Recursion in Models and Decision Making: Recursion in Exponential
Growth and Decay
IV.B Student Activity Sheet 3: Recursion and Exponential Functions
3. Tennis balls are sealed in a pressurized container to maintain the rebound percentage of
the balls. A tennis ball has a rebound percentage of 55% when it is taken out of the
pressurized can. Suppose a tennis ball is dropped from a height of 2 meters onto a tennis
court. Use the rebound rate given to predict the height of the ball's first seven bounces.
Bounce
No.
0
Process
(initial drop height given)
Height
(m)
2
1
0.55*2
1.1
2
0.55*1.1
0.605
3
0.55*0.605
0.3328
4
0.55*0.3328
0.1830
5
0.55*0.1830
0.1007
6
0.55*0.1007
0.0554
7
0.55*0.0554
0.0305
4. Write a recursive rule for the height of the ball for each successive bounce.
We can know that a1 = 2. Then
𝑎1 = 2
𝑎2 = 1.1
𝑎3 = 0.605
.
.
.
𝒂𝒏 = 𝒂𝒏𝟕 ∗ 𝟎. 𝟓𝟓
Then, the recursive rule for the height of the ball for each successive bounce is a n = an7*0.55
Charles A. Dana Center at The University of Texas at Austin
Advanced Mathematical Decision Making (2010)
Activity Sheet 3, 5 pages
11
Student:
Class:
Date:
Using Recursion in Models and Decision Making: Recursion in Exponential
Growth and Decay
IV.B Student Activity Sheet 3: Recursion and Exponential Functions
5. Describe, in words, how the height of each bounce is calculated from the height of the
previous bounce.
The height of each bounce is calculated taking the last height bounce and then it is
multiplied by 0.55 (55%), starting by the first height (the known height), it would be ...
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Advanced Mathematical Decision Making 2010 Activity Sheet 12 Answers
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