Check for Understanding
A super-ball has a 75% rebound ratio-that is, when it bounces repeatedly, each bounce is 75% as high as the previous bounce. When you drop it from a height of 20
feet how high does the ball bounce on the eighteenth bounce? Round your answer to the nearest hundredths.

0.11 feet

Step-by-step explanation:

Every bounce, the ball bounces to 75% of its previous bounce, so the first few bounces will give us heights of

20 ft (0 bounces)

20 × 0.75 = 15 ft (1 bounce)

20 × 0.75 × 0.75 = 11.25 ft (2 bounces)

We can express the continued multiplication by 0.75 as an exponent, so that after the nth bounce, the ball will bounce feet. Plugging in 18 for n gets us

feet.

answer: the answer is 35%