A treatment protocol for a disease in children involves long-term infusion of an appropriate medication. The concentration of the medication in the blood over time is modeled by the function $C$ defined on the interval $[0; +\infty[$ by:

$$C ( t ) = \frac { d } { a } \left( 1 - \mathrm { e } ^ { - \frac { a } { 80 } t } \right)$$

The clearance $a$ of a certain patient is 7, and we choose an infusion rate $d$ equal to 84. In this part, the function $C$ is therefore defined on $[0; +\infty[$ by:

$$C ( t ) = 12 \left( 1 - \mathrm { e } ^ { - \frac { 7 } { 80 } t } \right)$$

\begin{enumerate}
  \item Study the monotonicity of the function $C$ on $[0; +\infty[$.
  \item For the treatment to be effective, the plateau must equal 15. Is the treatment of this patient effective?
\end{enumerate}