Answer: p = 25%
Step-by-step explanation:
Since each time the ball bounces, it rebounds to p% of its previous height, it means that the height of rebound is decreasing in geometric progression. Also, the ball had innumerable bounces. We would apply the formula for determining the sum of an infinite geometric sequence which is expressed as
S = a/(1 - r)
a represents the initial height of the ball.
r represents the common ratio by which the height of each rebound is decreasing.
S represents the total distance that the ball travels.
a = 80 feet
S = 320 feet
Therefore,
320 = 80/(1 - r)
1 - r = 80/320 = 0.25
The percentage p by which the height of each rebound is decreasing is
0.25 × 100 = 25%
