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