Final answer:
To calculate the height of the 6th bounce when the ball bounces at 50% of its previous height each time, we use the formula for a geometric sequence. The height of the 6th bounce is 0.625 feet.
Step-by-step explanation:
When John drops a ball off a building and it bounces 20 feet on the first bounce, and then bounces 50% of its original height on subsequent bounces, we can use a geometric progression to find the height of the 6th bounce.
The height of the bounce can be found using the formula height of the nth bounce = initial height × (bounce factor)n-1, where bounce factor is 0.5 for 50% of the height.
So, the height of the 6th bounce would be 20 × (0.5)6-1 = 20 × (0.5)5 = 20 × 0.03125 = 0.625 feet. Therefore, the answer is D. 0.625 feet.