Application

Question

To test the bounce of a racquetball, the ball is dropped from a
height of 8 feet. The ball is judged “good” if it rebounds at least
75% of its previous height with each bounce. Write out the
first six terms of this geometric sequence (round to the nearest
tenth). Determine if a ball is “good” that rebounds to a height
of 2.5 feet after the fifth bounce.

Answer 1

Each bounce is 75% of the previous height

 

8 x .75 = 6ft for first bounce

 

6 x .75 = 4.5 for the second bounce

 

4.5 x .75  = 3.375

 

3.375 x .75  = 2.53 for the fourth

 

2.53 x .75  = 1.90 for the fifth bounce.

 

So a ball that bounces 2.50 feet on the 5th bounce is a good ball.

 

Math formula is height = 8(.75ⁿ) where n is the number of bounces.