A ball is dropped from an initial height of 22 feet and bounces off the ground repeatedly. The function h

Question

A ball is dropped from an initial height of 22 feet and bounces off the ground repeatedly. The function h estimates that the maximum height reached after each time the ball hits the ground is 85 % of the maximum height reached after the previous time the ball hit the ground. Which equation defines h , where h ( n ) is the estimated maximum height of the ball after it has hit the ground n times and n is a whole number greater than 1 and less than 10 ?

Accepted Answer

Choice B is correct. It's given that for the function h , h n is the estimated maximum height, in feet, of the ball after it has hit the ground n times. It's also given that the function h estimates that the maximum height reached after each time the ball hits the ground is 85 % of the maximum height reached after the previous time the ball hit the ground. It follows that h is a decreasing exponential function that can be written in the form h n = a p 100 n , where a is the initial height, in feet, the ball was dropped from and the function estimates that the maximum height reached after each time the ball hits the ground is p % of the maximum height reached after the previous time the ball hit the ground. It's given that the ball is dropped from an initial height of 22 feet. Therefore, a = 22 . Since the function h estimates that the maximum height reached after each time the ball hits the ground is 85 % of the maximum height reached after the previous time the ball hit the ground, p = 85 . Substituting 22 for a and 85 for p in the equation h n = a p 100 n yields h n = 22 85 100 n , or h n = 22 0.85 n . Choice A is incorrect. This function estimates that the maximum height reached after each time the ball hits the ground is 22 % , not 85 % , of the maximum height reached after the previous time the ball hit the ground. Choice C is incorrect. This function estimates that the ball is dropped from an initial height of 85 feet, not 22 feet, and that the maximum height reached after each time the ball hits the ground is 22 % , not 85 % , of the maximum height reached after the previous time the ball hit the ground. Choice D is incorrect. This function estimates that the ball is dropped from an initial height of 85 feet, not 22 feet.

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