SOLUTION: A ball is dropped from 10 feet high and always bounces back up half the distance it just fell. After how many bounces will the ball first reach a maximum height less than 1 foot?

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Question 232800: A ball is dropped from 10 feet high and always bounces back up half the distance it just fell. After how many bounces will the ball first reach a maximum height less than 1 foot?
Answer by Alan3354(69443) About Me  (Show Source):
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A ball is dropped from 10 feet high and always bounces back up half the distance it just fell. After how many bounces will the ball first reach a maximum height less than 1 foot?
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B ht
1 5
2 2.5
3 1.25
4 0.625
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On the 4th bounce.
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h = 10*(1/2)^n
Use 1 to find n
10*(1/2)^n = 1
(1/2)^n = 0.1
n*log(0.5) = log(0.1)
n = log(0.1)/log(0.5)
n = ~ 3.32
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The nearest next bounce is 4.