Final answer:
To calculate how long it will take for Xanax to decay to 90% of the original dosage, we use the formula for exponential decay in relation to the half-life of the substance. Given that the half-life of Xanax is 36 hours, we solve for the time that corresponds to the remaining amount being 90% of the initial dosage.
Step-by-step explanation:
The question pertains to the decay of a dosage of Xanax over time based on its half-life. Given that the half-life of Xanax is 36 hours, we need to determine how long it will take for the drug to decay to 90% of the original dosage. This involves a basic understanding of exponential decay and half-life calculations.
To find the time it takes for a substance to decrease to a certain percentage of its original amount, we can use the formula that relates the remaining quantity of a substance to time and the half-life of the substance:
N(t) = N0(1/2)^(t/T),
where N(t) is the remaining amount at time t, N0 is the initial amount, and T is the half-life. When the remaining amount is 90% of the initial amount, we have:
0.90 = (1/2)^(t/36)
To solve for t, we can take the logarithm of both sides of the equation. In this case, we are looking for a decay, not a half-life, so the time will be less than one half-life.
After solving the equation, we can determine the time t that corresponds to the 90% remaining dosage.