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?

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.