Mathematics

Mathematics

Problem

A patient has a drug concentration C(0)=10 mg/LC(0)=10\,\text{mg/L} in the bloodstream at t=0t=0 hours. For 0≤t<20\le t<2 hours, the concentration satisfies dCdt=0.5C\dfrac{dC}{dt}=0.5C. After t=2t=2 hours the drug metabolizes so that dCdt=−0.25C\dfrac{dC}{dt}=-0.25C. At what time t>2t>2 (in hours) does the concentration return to 10 mg/L10\,\text{mg/L}? a) 4 b) 10 c) 6 d) 8

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