A certain drug is eliminated from the bloodstream exponentially with a half-life of 60 hours. Suppose that a patient receives an initial dose of 10 milligrams of the drug at midnight. Estimate
When the drug concentration will reach 20% of its initial level.
A)139 hours
B)199 hours
C)79 hours
D)23 hours

Question

Quizplus · Accepted Answer

The drug's concentration decreases exponentially, following the formula $C = C_0 \times (1/2)^{t/T}$, where $C$ is the final concentration, $C_0$ is the initial concentration, $T$ is the half-life, and $t$ is the time in hours. To find when the concentration reaches 20% of its initial level, we set $C = 0.2C_0$ and solve for $t$, using $T = 60$ hours. This gives us $0.2 = (1/2)^{t/60}$. Solving for $t$, we find that $t \approx 139$ hours.

A Certain Drug Is Eliminated from the Bloodstream Exponentially with a Half-Life