Aball is dropped from a height of 36 feet. at each bounce the ball reaches a height that is three quarters of the previous height. how many bounces must the ball make before it rebounds less than 1 foot?

Ball will make 13 bounces before it rebounds less than 1 foot.

Step-by-step explanation:

A ball is dropped from a height of 36 feet.

In each bounce the ball reaches a height that is three quarters of the previous height.

Sequence formed will be 36, 27, 20.25.........

This sequence has a common ratio of

Therefore, sequence will be a geometric sequence.

Explicit formula of this sequence will be

where a = first term of the sequence

r = common ratio

n = number of term

For this sequence formula will be

If this term is less than 1

Taking log on both the sides

1.5563 + n(-0.1249) < 0

0.1249n > 1.5563

n >

n > 12.46

n ≈ 13

Therefore, ball will make 13 bounces before it rebounds less than 1 foot.

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