The height h(n) of a bouncing ball is an exponential function of the number n of bounces. One ball is dropped and on the first bounce reaches a height of 6 feet. On the second

bounce it reaches a height of 4 feet.

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The height of a bouncing ball is defined by .

Step-by-step explanation:

According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:

, , (1)

Where:

- Height reached by the ball on the first bounce, measured in feet.

- Decrease rate, no unit.

- Number of bounces, no unit.

- Height reached by the ball on the n-th bounce, measured in feet.

The decrease rate is the ratio between heights of two consecutive bounces, that is:

(2)

Where is the height reached by the ball on the second bounce, measured in feet.

If we know that and , then the expression for the height of the bouncing ball is:

The height of a bouncing ball is defined by .

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step-by-step explanation: