Question

1) The concentration C of a certain drug in a patients blood stream t hours after the injection is given by
C(t)=t
-----
2t^2+1

find the horizontal asymptote of C(t)
What happens to the concentration of the drug as t increases?

Answer 1

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 \(t\to\infty\). If \(t\) approaches a certain value, then you say the horizontal asymptote is at the line \(y=\text{certain value}\).

What you need to do: Evaluate
\[\lim_{t\to\infty}C(t)\]