Question

A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.

Answer 1

Sample Response: There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.

Answer 2

If x is the peak of the ball and y is the peak of the previous bounce, the formula can be used below to describe the sequence:

y * (2/3) = x
12 * (2/3) = x
8 = x

The ball reaches 8 ft on its fourth bounce.