A drug is administered intravenously at a constant rate of $r$ mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality $k>0$.

(a) Set up a differential equation for the quantity, $Q$, in milligrams, of the drug in the body at time $t$ hours. Your answer will contain the unknown constants $r$ and $k$.
$Q^{\,\prime} =$

(b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain $r$ and $k$.
$Q =$

(c) What is the limiting long-run value of $Q$?
$\displaystyle \lim_{t\to\infty} Q(t) =$