Question

A ball that dropped from a height of 729 cm rebounds on each bounce one-third of the distance from which it fell. How high does it go on the 7th rebound?
A. 0.33 cm
B. 0.67 cm
C. 0.25 cm
D. 0.11 cm

Answer 1

the first bounce will only go 1/3 of the original height

the 2nd bounce will only go 1/3 of the height of the first bounce
or 1/9 of the original height (1/3 * 1/3)

the 3rd bounce will go 1/3 of the height of the 2nd bounce, or 1/9 of the height of the first bounce, or 1/27 of the height of the original height

using this pattern, we can write an equation to mimic this pattern

Answer 2

since it multiplies by 1/3 for each bounce, we can write it as

\[(\frac{1}{3}) ^ n\]
where n would be the number of bounces

Answer 3

if we multiply this by the original height, we can get an equation for how high the ball will bounce for the nth bounce

\[y = y_0 (\frac{1}{3})^n\]