Answer:
[tex]H_{n} = 30(0.8)^{n}[/tex]
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 [tex]H_{n} = 30(0.8)^{n}[/tex]
So, after 6th bounce the maximum height will be [tex]H_{6} = 30(0.8)^{6} = 7.864[/tex] feet = 7 feet 10 inches (Appx.)
