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25 April, 22:32

A Super Happy Fun Ball is dropped from a height of 10 feet and rebounds 13/14 of the distance from which it fell. How many times will it bounce before its rebound is less than 1 foot? It will bounce times before its rebound is less than 1 foot.

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  1. 26 April, 02:19
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    32

    Explanation:

    First bounce = 13 / 14 * 10 = 130 / 14

    using geometric progression where the common ratio = 13/14, the first bound = 130/14

    ar^n-1 < 1

    substitute the values into the equation

    130 / 14 * 13/14^ (n-1) < 1

    (13/14) ^n-1 < 1: (130/14)

    (13/14) ^n-1 < 14 / 130

    take log of both side

    log (13 / 14) ^n-1 < log (14/130)

    n-1 log (13 / 14) < log (14/130)

    since log (13/14) negative

    n-1 > (log (14/130)) : (log (13/14)

    n - 1 > 30.07

    n > 30.07 + 1 > 31.07

    The 32 bounce will the first less than 1 foot
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