Question

When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream after t minutes is given by
C(t) = 0.06t − 0.0002t2,
where 0 ≤ t ≤ 240 and the concentration is measured in mg/L.

When is the maximum serum concentration reached?
t =______ min

What is the maximum concentration?
________mg/L

Answer 1

The time when the maximum serum concentration is reached is obtained by equating the derivative of C(t) to 0.
i.e. dC(t)/dt = 0.06 - 2(0.0002t) = 0.06 - 0.0004t = 0
0.0004t = 0.06
t = 0.06/0.0004 = 150
Therefore, the maximum serum concentration is reached at t = 150 mins

The maximum concentration = 0.06(150) - 0.0002(150)^2 = 9 - 0.0002(22,500) = 9 - 4.5 = 4.5
Therefore, the maximum concentration is 4.5mg/L