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

Answer:

$H_{n} = 30(0.8)^{n}$

7 feet 10 inches

Step-by-step 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.)