Saturday, May 21, 2016

College Algebra, Chapter 4, 4.1, Section 4.1, Problem 68

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)=0.06t0.0002t2, where 0t240 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.

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