A ball rebounds one-half the distance that it falls. If the ball is dropped from a height of 512 feet, how high does it go on its 8th rebound?

Answer 1

As you might suspect since you're on the chapter on exponential functions, this situation can be modeled with an exponential equation (or a geometric sequence):

h(n) = a·bⁿ

1. h(n) = height on bounce n
2. a = starting height = 512 ft
3. b = common ratio = 1/2
4. n = number of bounces = 8, where n is an integer

h(n) = 512·(1/2)ⁿ

h(8) = 512·(1/2)⁸

Plug in the numbers and compute the answer.