Question

A ball is dropped from a height of 30 feet. The ball bounces. After each bounce, the maximum height of the ball is 80% of the previous height. Write an nth term formula to model the situation and approximate the maximum height of the ball after 6 bounces.

A. 8 feet 3.5 inches
B. 7 feet 10 inches
C. 9 feet 10 inches
D. 6 feet 3.5 inches

Answer 1

`H_(n) = 30(0.8)^(n)`

7 feet 10 inches

Explanation:

A ball is falling from a height of 30 feet and then it bounces. After each bounce, the maximum height of the ball is 80% of the previous height.

So, after 1st bounce, the maximum height was (0.8 × 30) feet.

Similarly, after 2nd bounce, the maximum height was 0.8(0.8 × 30) feet.

In this way, the maximum height of the ball after nth bounce will be
`H_(n) = 30(0.8)^(n)`

So, after 6th bounce the maximum height will be
`H_(6) = 30(0.8)^(6) = 7.864` feet = 7 feet 10 inches (Appx.)