A patient has a drug concentration in the bloodstream at hours

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A patient has a drug concentration

C(0)=10\,\text{mg/L}

in the bloodstream at

t=0

hours. For

0\le t<2

hours, the concentration satisfies

\dfrac{dC}{dt}=0.5C

. After

t=2

hours the drug metabolizes so that

\dfrac{dC}{dt}=-0.25C

. At what time

t>2

(in hours) does the concentration return to

10\,\text{mg/L}

? (a) 4 (b) 10 (c) 6 (d) 8