Question

A certain ball is dropped from 204 centimeters, and has a rebound factor of 72% (The height of the ball after each bounce is 72% of the height of the bounce before.). Which equation represents the relationship between the the number of bounces, n, and height, h, in centimeters? Group of answer choices

Answer 1

The equation that represents the relationship between the number of bounces and the height is
`H = 204\cdot 0.72^(n)`.

Explanation:

According to this exercise, we notice that maximum height of the ball (
`H`), measured in centimeters, is reduced at geometric rate and as a function of the number of bounces (
`n`), with no unit, which is defined by geometric progression:

`H = H_(o)\cdot r^(n)` (1)

Where:

`H_(o)` - Initial height of the ball, measured in centimeters.

`r` - Bounce factor, no unit.

If we know that
`H_(o) = 204\,cm` and
`r = 0.72`, then the equation that represents the relationship between the number of bounces and the height is:

`H = 204\cdot 0.72^(n)` (2)