A super ball is thrown of a building that is 800ft tall. After each bounce the ball loses 30% of its energy so that the height is 70% of what it was the previous bounce. How many bounces before the superball’s maxium height is less than 1ft
Height after bounce 1 = 800(.7)
height after bounce 2 = 800(.7)^2
800(.7)^n < 1
.7^n < .00125
take logs of both sides, then use log rules
n log.7 < log .00125
n < log .00125/log .7
n < 18.7
check :
after 18 bounces , height = 1.3 ft
after 19 bounces, height = .91 ft
so it will take 19 bounces for the height to be less than 1 ft