*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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## 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 continues to rebound to a height that is 70 percent of the highest point of the previous bounce. The graph below illustrates these maximum heights.

Because each successive maximum height is found by multiplying the previous height by the same value, this is a geometric sequence. The maximum height can also be expressed as an exponential function, with the **domain** restricted to **whole numbers...**

This section contains 895 words(approx. 3 pages at 300 words per page) |