Find the total distance traveled by a ball, given its starting height and the percent of its height that it rebounds to after bouncing. Round to the nearest tenth of a foot if necessary.
-Starting height: 200 feet; rebounds $15 \%$
A) 1533.3 feet
B) 173.9 feet
C) 270.6 feet
D) 235.3 feet

Question

Quizplus · Accepted Answer

The ball travels 200 feet down initially. After each bounce, it travels up and down 15% of the previous height. The total distance is the sum of these distances, calculated as an infinite geometric series: 200 + 2(200)(0.15) + 2(200)(0.15)^2 + ... = 200 + 2(30) + 2(4.5) + ... = 200 + 60 + 9 + ... = 270.6 feet.

Find the Total Distance Traveled by a Ball, Given Its 15%15 \%15%

Find the Total Distance Traveled by a Ball, Given Its $15 \%$