Question

Check for Understanding

Answer 1

Answer:

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 $20(0.75)^{n}$ feet. Plugging in 18 for n gets us

$20(0.75)^{18}\approx 0.11$ feet.