SOLUTION: 1) When a ball is dropped to the floor it bounces to 4/5th of the height from which it has been dropped. If it is dropped from a height of 2 meters, after how many bounces will its

Algebra ->  Sequences-and-series -> SOLUTION: 1) When a ball is dropped to the floor it bounces to 4/5th of the height from which it has been dropped. If it is dropped from a height of 2 meters, after how many bounces will its      Log On


   

Question 289917: 1) When a ball is dropped to the floor it bounces to 4/5th of the height from which it has been dropped. If it is dropped from a height of 2 meters, after how many bounces will its height go below ½ a meter?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
n=0,First height, Zero bounces = h%280%29=2
n=1,Second height, 1 bounce = h%281%29%284%2F5%292=8%2F5
n=2,Third height, 2 bounces = h%282%29=%284%2F5%29%288%2F5%29=%284%2F5%29%284%2F5%292=%284%2F5%29%5E2%2A2
n=3,Fourth height, 3 bounces = h%283%29=%284%2F5%29%5E3%2A2
You are looking for heights less than 1/2.
h%28n%29=%284%2F5%29%5En%2A2=1%2F2
%284%2F5%29%5En=1%2F4
Take the log base (4/5) of each side,
n=log%280.8%2C0.25%29=log%2810%2C0.25%29%2Flog%2810%2C0.8%29
n=6.2
Take the next integer bounce, n=7
On the seventh bounce the height will be less than (1/2).
h=%284%2F5%29%5E7%2A2=0.42