Problem

Bounce height is \(H(n)~=~10\cdot~0.6^{n}~\text{feet}\) after bounce number \(n~\in~{0,~1,~2,~\ldots~}\). Interpret the domain and output, initial height, retained and lost percentages, horizontal asymptote, and finite-zero behavior.

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input = n all real numbers; output = H(n) feet; initial = H(0)=10 feet; retained = 60% each bounce; lost = 40% each bounce; asymptote = y=0 feet; finite-zero = fractional bounces are required

input = n whole bounce number; output = H(n) feet; initial = H(0)=10 feet; retained = 60% each bounce; lost = 40% each bounce; asymptote = y=0 feet; finite-zero = ideal model approaches but never equals 0 at a finite bounce

input = n whole bounce number; output = H(n) feet; initial = H(0)=10 feet; retained = 40% each bounce; lost = 60% each bounce; asymptote = y=0 feet; finite-zero = ideal model approaches but never equals 0 at a finite bounce

input = n whole bounce number; output = H(n) feet; initial = H(0)=0.6 feet; retained = 10% each bounce; lost = 90% each bounce; asymptote = n=0; finite-zero = height equals 0 after 10 bounces

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Bounce height is \(H(n)~=~10\cdot~0.6^{n}~\text{feet}\) after bounce number \(n~\in~{0,~1,~2,~\ldots~}\). Interpret the domain and output, initial height, retained and lost percentages, horizontal asymptote, and finite-zero behavior.

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