The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of 73 minutes.Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 1.3/μgmL. What will the concentration be 146 minutes later?Round your answer to 2 significant digits.
Question
The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of 73 minutes.Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 1.3/μgmL. What will the concentration be 146 minutes later?Round your answer to 2 significant digits.
Solution
First, we need to understand that first-order kinetics means that the rate of elimination of the drug is directly proportional to the concentration of the drug in the body.
The formula for first-order kinetics is:
Ct = C0 * (1/2)^(t/t1/2)
where: Ct = concentration of the drug at time t C0 = initial concentration of the drug t = time t1/2 = half-life of the drug
Given in the problem: C0 = 1.3 μg/mL t = 146 minutes t1/2 = 73 minutes
Substitute these values into the formula:
Ct = 1.3 * (1/2)^(146/73)
Simplify the exponent:
Ct = 1.3 * (1/2)^2
Calculate the final concentration:
Ct = 1.3 * 0.25 = 0.325 μg/mL
So, the concentration of the drug in the bloodstream 146 minutes after injection will be approximately 0.33 μg/mL when rounded to two significant digits.
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