Answer:
The equation that represents the relationship between the number of bounces and the height is [tex]H = 204\cdot 0.72^{n}[/tex].
Step-by-step explanation:
According to this exercise, we notice that maximum height of the ball ([tex]H[/tex]), measured in centimeters, is reduced at geometric rate and as a function of the number of bounces ([tex]n[/tex]), with no unit, which is defined by geometric progression:
[tex]H = H_{o}\cdot r^{n}[/tex] (1)
Where:
[tex]H_{o}[/tex] - Initial height of the ball, measured in centimeters.
[tex]r[/tex] - Bounce factor, no unit.
If we know that [tex]H_{o} = 204\,cm[/tex] and [tex]r = 0.72[/tex], then the equation that represents the relationship between the number of bounces and the height is:
[tex]H = 204\cdot 0.72^{n}[/tex] (2)
