Problem

Medicine amount is \(A(t)~=~1200\cdot~0.75^{t}~\text{milligrams}\) \(t~\text{hours}\) after dosing. Interpret the input and output, initial amount, hourly retained and decreased percentages, horizontal asymptote, and finite-zero behavior.

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input = t hours; output = A(t) milligrams; initial = A(0)=1200 mg; retained = 25% each hour; decreased = 75% each hour; asymptote = y=0 mg; finite-zero = the ideal model approaches but never equals 0 for finite t

input = t hours; output = A(t) milligrams; initial = A(0)=1200 mg; retained = 75% each hour; decreased = 25% each hour; asymptote = t=0 hours; finite-zero = amount equals 0 after 4 hours

input = t hours; output = A(t) milligrams; initial = A(0)=0.75 mg; retained = 1200% each hour; decreased = negative 1100% each hour; asymptote = y=1200 mg; finite-zero = amount starts at zero

input = t hours; output = A(t) milligrams; initial = A(0)=1200 mg; retained = 75% each hour; decreased = 25% each hour; asymptote = y=0 mg; finite-zero = the ideal model approaches but never equals 0 for finite t

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Medicine amount is \(A(t)~=~1200\cdot~0.75^{t}~\text{milligrams}\) \(t~\text{hours}\) after dosing. Interpret the input and output, initial amount, hourly retained and decreased percentages, horizontal asymptote, and finite-zero behavior.

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