Mathematics

Problem

A patient is given a 100 mg intravenous dose of a drug at time

t=0

. The concentration of the drug in the bloodstream (in mg) decays exponentially and is modelled by

100 e^{-0.25 t}

, where

t

is in hours. After 6 hours, the patient receives a second identical 100 mg dose instantly. Which of the following functions

C(t)

correctly models the total drug concentration for

0\le t\le 12

hours? a)

C(t)=\begin{cases}100 e^{-0.25 t},&0\le t\le 6\\200 e^{-0.25(t-6)},&6<t\le 12\end{cases}

C(t)=\begin{cases}100 e^{-0.25 t},&0\le t\le 6\\100+100 e^{-0.25(t-6)},&6<t\le 12\end{cases}

C(t)=\begin{cases}100 e^{-0.25 t},&0\le t\le 6\\100 e^{-0.25 t}+100 e^{-0.25(t-6)},&6<t\le 12\end{cases}

C(t)=\begin{cases}100 e^{-0.25 t},&0\le t\le 6\\200 e^{-0.25 t},&6<t\le 12\end{cases}