Chapter 6, Problem 31P

The concentration of a drug in the body C_Pcan be modeled by the equation:

$C_P=\frac{D_G}{V_{dP}}\frac{k_a}{k_a-k_{ae}}(e^{-k_{e}t-e-k_{a}t})$

where DG is the dosage administered (mg), V_dis the volume of distribution (L), k_dis the absorption rate constant (h-1) k is the elimination rate constant (h-1), and t is the time (h) since the drug was administered. For a certain drug, the following quantities are given: D_G= 150mg, V_d, = 50L, k_a= 1.6 h-1, and k_e= 0.4 h-1.

(a) A single dose is administered at t = 0. Calculate and plot C_Pversus t for 10h.

(b) A first dose is administered at t = 0, and subsequently four more doses are administered at intervals of 4 h (i.e., at t = 4, 8, 12, 16). Calculate and plot C_P, versus t for 24 h.