Question

The quantity of a drug in the bloodsteam t hours after a tablet is swallowed is given, in mg, by q(t)=40((e^-t)-(e^-2t))
What is the maximum amount of the drug in the bloodstream at one time?

Answer 1

q(t) = 40((e^-t) - (e^-2t))
For q(t) to be maximum dq/dt = 0
dq/dt = 40(-(e^-t) + 2(e^-2t) = 0
2e^-2t - e^-t = 0
2e^-2t = e^-t
e^t = 2
t = ln 2

q(ln 2) = 40((e^(-ln 2) - (e^(-2ln 2)) = 40(1/2 - 1/4) = 40(1/4) = 10
Therefore, thw maximum amount of drug in the bloodstream at one time is 10 mg.