Q 3.3 (10 points) Given that you want to maintain plasma concentrations above 2.5 mg/L for 12 hours, what IV bolus dose would be needed if t_1/2 = 3.8 hr and V = 68.6 L? Assume a one compartment linear pharmacokinetic model. What would the expected Cp⁰ value be if this dose were given.

Cp = Cp⁰•e^-kel•t = (Dose/V) • e^-kel•t

Note: kel = ln2/3.8 = 0.182 hr^-1

2.5 = (Dose/68.6) • e^{-0.182 x 12}

Dose = (2.5 x 68.6) / e^-2.184 = 1523 mg

Cp⁰ = 1523 / 68.6 = 22.2 mg/L