When a certain drug is taken orally, the concentration of the drug in the patient

4mg/L

Step-by-step explanation:

Here is the complete 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) = 0.08t − 0.0004t2,  where  0 ≤ t ≤ 240 and the concentration is measured in mg/L.  When is the maximum serum concentration reached?

Given the concentration of the drug in the patient's bloodstream after t minutes modeled by the equation;

C(t) = 0.08t − 0.0004t^2

The maximum serum concentration is reached at when d(C(t))/dt = 0

d(C(t))/dt = 0.08-2(0.0004)t

d(C(t))/dt = 0.08-0.0008t

since d(C(t))/dt = 0

0 =  0.08-0.0008t

get the value of t

-0.08 = -0.0008t

t = 0.08/0.0008

t = 100secs

Get the maximum serum concentration reached by substituting t = 100s into the equation as shown;

C(t) = 0.08t − 0.0004t^2

C(100) = 0.08(100) − 0.0004(100)^2

C(t) = 8-0.0004(10000)

C(t) = 8-4

C(t) = 4mg/L

Hence the maximum serum concentration reached is 4mg/L