Question

Sharon drops a rubber ball from a height of 48 feet. Every bounce sends the ball half as high as it was before.

What is the total vertical (up and down) distance the ball has traveled, from the moment it is dropped to the moment it hits the floor for the fourth?

Answer 1

Answer:

Step-by-step explanation:

The function for this is exponential.  The model for this situation is

$y=48(.5)^x$

The first time the ball hits the ground, it is dropped from a height of 48 feet.  So its first travel downwards is 48 feet.

The second time the ball hits the ground, it falls from a height half of 48, which is 24.

The third time the ball hits the ground, it falls from a height half of 24, which is 12.

The fourth time the ball hits the ground, it falls from a height half of 12, which is 6.

In all, the ball has traveled 48 + 24 + 12 + 6 which is 90 feet total.

You could also use the exponential model to solve for the feet, y, after each drop, x.