When a ball bounces, different mathematical models can describe what happens. If the ball bounces in place several times, a geometric sequence or exponential model describes the maximum height that the ball attains in relation to the number of bounces. For any single bounce, a quadratic model describes the height of the ball at any point in time.

Exponential Model: Maximum Height

To examine the maximum height a bouncing ball attains, ignore external factors such as air resistance. A ball bounced in place recovers a certain percentage of its original height. For example, suppose a ball that recovers 70 percent of its height is dropped from 200 feet. The maximum height it reaches after its first bounce is 70 percent of 200 feet, or 140 feet. After the second bounce, it reaches a height of 70 percent of 140 feet, or 98 feet. In similar fashion, the ball...