A ball is dropped from a height of 10 feet and bounces. Each bounce is 3/4 of the height of the bounce before. Thus after the ball hits the floor for the first time, the ball rises to a height of 10 (3/4)= 7.5 feet, and after the it hits the floor for the second time, the ball rises to a height of 7.5(3/4)= 10 (3/4)^2= 5.625 feet. (a) Find an expression for the height to which the ball rises after it hits the floor for the nth time.
After it hits the floor for the nth ttime, the ball rises to a height of 10 (3/4)^n feet.
(b) Find an expression for the total vertical distance the ball has traveled when it hits the floor for the first, second, third, and fourth times.
After one time the ball has traveled 10 feet. After two times the ball has traveled 10 + 2.10 (3/4)^1 feet. After three times the ball has traveled
10 + 2.10 (3/4)^1+ 2 · 10 (3/4)^2 feet.
(c) Find an expression for the total vertical distance the ball has traveleled when it hits the floor for the nth time. Express your answer in a closed form.