Question

The height that a properly inflated basketball bounces decreases exponentially by 27.8% with each subsequent bounce after the initial drop. A local basketball league tests the inflation of their basketballs by dropping them from a height of 6 feet. Which equation can be used to model the height of the basketball, H, after b bounces?

Answer 1

`H (b) = 0.722^b(6)`

Explanation:

The first time the basketball bounces it reaches a height of
`(1-0.278)(6) = (0.722) (6)`.

The second time the basketball bounces it reaches a height of
`(0.722) (0.722) (6) = [(0.722) ^ 2] (6)`. Therefore, after b rebounds the height that the basketball will reach is given by:

`H (b) = 0.722^b(6)`