Since time is always moving forward, you can only have (t>0) (where (t=0) indicates the start time of an event, in this case injection of the drug).
This means you only need to check the end behavior of the function as t to infinity. If (t) approaches a certain value, then you say the horizontal asymptote is at the line (y=certain value). What you need to do: Evaluate limit of t to infinity / C(t)
