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The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of 57 minutes.Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 1.9/μgmL. What will the concentration be 228 minutes later?Round your answer to 2 significant digits.μgmL

Question

The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of 57 minutes.Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 1.9/μgmL. What will the concentration be 228 minutes later?Round your answer to 2 significant digits.μgmL

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Solution

The concentration of a drug in the body following first-order kinetics can be calculated using the formula:

C = C0 * (1/2)^(t/t1/2)

where: C is the final concentration of the drug, C0 is the initial concentration of the drug, t is the time elapsed, t1/2 is the half-life of the drug.

Given: C0 = 1.9 μg/mL, t = 228 minutes, t1/2 = 57 minutes.

Substituting these values into the formula, we get:

C = 1.9 * (1/2)^(228/57)

Solving this gives:

C = 1.9 * (1/2)^4

C = 1.9 * 0.0625

C = 0.11875 μg/mL

Rounding this to two significant digits gives a final concentration of 0.12 μg/mL.

This problem has been solved

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