a bouncy ball rebounds to 90% of the height of the preceding bounce. jason drops a bouncy ball from initial height of 25 feet

Question

(a) write out the sequence of the height of the first 4 bounces.
(b) derive an explicit formula for the rebound height of a bouncy ball dropped from an intial height of 25 feet.

Answer 1

initial height = 25 ft
height after 1 bounce = 25(.9)
height after 2 bounces = 25(9)^2
height after 3 bounces = 25(.9)^3
height after 4 bounces = 25(.9)^4
..
height of ball after nth bounce = 25(.9)^n