the question is in the description because it's long

Question

A rubber ball bounces exactly half as high as it did in the previous bounce. It bounces 128 feet high on the first bounce. How high does it bounce on the 12th bounce? Express your answer as a common fraction

Answer 1

It helps to set up a table.

 

Bounce Height

______ _____

 

1          128

2          (1/2)128

3          (1/2)(1/2)128 = (1/2)²128 = (1/2)^3-1128

4          (1/2)(1/2)^3-1128 = (1/2)^4-1128

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(note the pattern)

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n          (1/2)^n-1128

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Then the height of the 12th bounce must be

 

h₁₂ = (1/2)^12-1128 = (1/2)¹¹128 = 1/16 ft