Suppose a a certain drug is taken orally, the concentration of the drug in the patient's blood stream 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, and what is that maximum concentration?
The function C is a quadratic function with a=−0.0002 and b=0.06. Thus, its maximum value occurs when
t=−b2a=−0.062(−0.0002)=150 min.
The maximum concentration is C(150)=0.06(150)−0.0002(150)2=4.5 mg/L.
So the serum will reached maximum concentration is 150 min. and the maximum concentration of serum is 4.5 mg/L.
Saturday, May 21, 2016
College Algebra, Chapter 4, 4.1, Section 4.1, Problem 68
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