A ball is dropped from 10 feet high and always bounces back up half the distance it just fell. After how many bounces will the ball first reach a maximum height less than 1 foot?
We can start by calculating the first few bounces. Yes, let's see what happens on the first bounce. So, the ball is dropped and it bounces back up 5 feet. Now let's see what happens on the second bounce. The ball is dropped from 5 feet and bounces back up 2.5 feet. Next bounce. The ball is dropped from 2.5 feet and bounces back up 1.25 feet. Now let's see what happens on the fourth bounce. The ball is dropped from 1.25 feet and bounces back up 0.625 feet. That's correct.

