The rate at which a particular medication leaves an individual's bloodstream is proportional to the amount of this medication that is in the bloodstream. An individual takes $275$ milligrams of the drug initially. The amount of medication is halved every $14$ hours. Approximately how many milligrams of the medication remain in the individual's bloodstream after $8$ hours?
$$Q(t)= Q_0 \, e^{kt}$$
where $Q_0$ is the initial amount, i.e. $275$, and $k$ is what I'm having trouble finding. It just says "halved every 14 hours" and that parts really confusing me.
The half time is the same over overy period, in particular from $t=0$ to $t=14$.
So we know $$Q(14) = \frac{1}{2}Q_0$$ which implies (afer dividing by $Q_0 >0$ on both sides ):
$$e^{14k} = \frac{1}{2} \implies 14k = \ln(\frac{1}{2}) $$
from which $k$ follows etc.