The recursive function of a ball with a 67% rebound is a(n) = 0.67a(n-1)
The recursive function of a ball
The rebound is given as:
r = 67%
Express as decimal
r = 0.67
So, the recursive function is:
a(n) = Previous height * r
This gives
a(n) = a(n-1) * 0.67
Evaluate
a(n) = 0.67a(n-1)
Hence, the recursive function is a(n) = 0.67a(n-1)
Complete the table
Basketball
The initial height is given as:
a(1) = 54
So, we have:
a(2) = 0.67 * 54 = 36.18
a(3) = 0.67 * 36.18 = 24.24
Tennis ball
The initial height is given as:
a(1) = 58
So, we have:
a(2) = 0.67 * 58 = 38.86
a(3) = 0.67 * 38.86 = 26.04
Table-tennis ball
The initial height is given as:
a(1) = 26
So, we have:
a(2) = 0.67 * 26 = 17.42
a(3) = 0.67 * 17.42 = 11.67
Hence, the complete table is:
Bounce n Height
First bounce 1 Basketball: 54 inches
Tennis ball: 58 inches
Table tennis ball: 26 inches
Second bounce 2 Basketball: 36.18 inches
Tennis ball: 38.86 inches
Table tennis ball: 17.42 inches
Third bounce 3 Basketball: 24.24 inches
Tennis ball: 26.04 inches
Table tennis ball: 11.67 inches
Read more about geometric functions at:
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Missing part of the question
A ball is dropped such that each successive bounce is 67% of the previous bounce's height.
