The concentration, C, in ng/ml, of a drug in the blood as a function of the time, t, in hours since the drug was administered is given by C = 15te-0.2t. The area under the concentration curve is a measure of the overall effect of the drug on the body, called the bioavailability. Find the bioavailability of the drug between t = 0 and t = 3

The bioavailability is 45.713 ng/ml

Step-by-step explanation:

The bioavailability can be calculated by integrating the concentration over the range 0 to 3

C=15∫te^ (-0.2t) dt

Using integration by part ∫udv=uv-∫vdu

u=t; du=dt

dv=e^ (-0.2t) dt; v = (-e^ (-0.2t)) / 0.2=-5e^ (-0.2t)

C=15[-5te^ (-0.2t) + 5∫te^ (-0.2t) ]

C=15[-5te^ (-0.2t) - 25e^ (-0.2t) ]

putting the limits t = 0 and 3

C=-75 (8e^ (-0.6) - 5)

C=45.713 ng/ml