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

Answer:

The equation that represents the relationship between the number of bounces and the height is $H = 204\cdot 0.72^{n}$.

Step-by-step 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)