A rubber ball is dropped from seven feet. After each bounce, it reaches the maximum height that is three fifths of the maximum height reached on the previous bounce. Let M(n) be the ball’s maximum height after the nth bounce. (a) Find an expression describing M(n) in terms of n. (b) Graph y = M(n). (c) At least roughly, after how many bounces, does the maximum height of the ball no longer exceeds 1 inch? (d) By what percentage does the maximum height change after each bounce? Is this percentage ’visible’ in your answer to part a)?
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A rubber ball is dropped from seven feet. After each bounce, it reaches the maximum height that is three fifths of the maximum height reached on the previous bounce. Let M(n) be the ball’s maximum height after the nth bounce.
(a) Find an expression describing M(n) in terms of n.
(b) Graph y = M(n).
(c) At least roughly, after how many bounces, does the maximum height of the ball no longer
exceeds 1 inch?
(d) By what percentage does the maximum height change after each bounce? Is this percentage ’visible’ in your answer to part a)?
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