We might think that a ball that is dropped from a height of 14 feet and rebounds to a height 3/4 of its previous height at each bounce keeps bouncing forever since it takes infinitely many bounces. This is not true! We examine this idea in this problem.

A. Show that a ball dropped from a height feet reaches the floor in seconds. Then use this result to find the time, in seconds, the ball has been bouncing when it hits the floor for the first, second, third and fourth times:
time at first bounce =
time at second bounce =
time at third bounce =
time at fourth bounce =

B. How long, in seconds, has the ball been bouncing when it hits the floor for the th time (find a closed form expression)?
time at th bounce =

C. What is the total time that the ball bounces for?
total time =

You can earn partial credit on this problem.