Solution

A patient receives an IV bolus dose of a drug. The concentration in the blood is modeled by $C(t) = 12e^{-0.3t}\ (\text{mg/L})$ where $t$ is the time in hours since that dose was taken. The minimum effective concentration (MEC) is $3\ \text{mg/L}$. The drug is considered effective if total AUC in a 24-hour period is at least $150\ \text{mg}\cdot\text{h}/\text{L}$.