Question

Christopher drops a ball from the roof of a 100 foot tall building. He predicts that after each time the ball bounces it will reach a maximum height of 12 the maximum height before the bounce. The expression 100⋅(12)3 gives the predicted maximum height of the ball after 3 bounces. What is the maximum predicted height of the ball after 3 bounces? Round to the nearest tenth, if necessary. 12.5 ft 16.7 ft 25 ft 50 ft

Answer 1

(a) 12.5 ft

Explanation:

The decay of the maximum height can be modeled by an exponential function of the form ...

y = a·b^x

where a is the initial height, and b is the "growth factor" that relates the bounce height to the drop height.

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We are given an initial height a=100, and a "growth factor" of 1/2, so the height after x bounces will be ...

y = 100·(1/2)^x

After 3 bounces, the maximum height is ...

y = 100·(1/2)^3 = 100/8 = 12.5

The height after 3 bounces is predicted to be 12.5 ft.