Use the exponential decay model, A=A0ekt to solve the following: A tranquilizer is used in the short-term relief of symptoms of anxiety. Its half-life in the bloodstream is 31 hours. How long will it take for the tranquilizer to decay to 90% of the original dosage?
The tranquilizer will take approximately 4.712 hours to decay to 90% of the original dosage.
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We are told that a drug decays in a person's system according to the decay model `A=A_0e^(kt)` . Here, A is the amount of the drug present after t hours, `A_0` (read as A nought) is the initial amount of the drug, e is the base of the exponential function (`e~~2.71828` ), k is the decay factor (or decay constant), and t is the amount of time in hours.
We are also told that the half-life of the drug in a person's system is 31 hours. This means that 31 hours after the dose is administered, 1/2 of the dose is still present.
We are asked to find the amount of...
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