A ball bounces 0.7 of the distance it is dropped. How many bounces will the ball make from a height of 1 meter if a bounce of less than 1 centimeter is to be ignored?

Answer 1

consider the first term to be
.7(1) = .7
term 2 = .7^2 = .49

what term = .01

.7^n = .01
n ln .7 = ln .01
n = ln.01/ln.7 = 12.9

term 12 = .7^12 = .0138 > .01
term 13 = .7^13 = .00968 < .01