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.

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