algebra word problem

Question

Drug concentration. The concentration C of a certain drug in a patient’s bloodstream hour after injection is given by C (t) = t/2t^2 +1 Find the horizontal asymptote (t). What happens to the concentration of the drug as t increases?

When I graph it, the horizontal asymptote appears to be y=0. The graph shows that as time increases, the concentration of the drug decreases to zero.

C(t) = t / (2t2 + 1)

As t →∝, t / (2t2 + 1) → 0

The horizontal asymptote is C (t) = 0.

As time passes, the concentration diminishes.

Domain: (−∞,∞),{t|t∈R}

Range: (−∞,∞),{t|t∈R

I cannot find the oblique asymptote 

Answer 1

Hola Lewis. First, it looks like you have answered this word problem correctly.

Second, is your question, "What is the oblique asymptote"? If so, you may be overthinking this one. I say this because: (1) I don't see the oblique asymptote mentioned anywhere in the word problem, and (2) there is no oblique asymptote in the graph for `C(t) = t / (2t2 + 1)`.

Does that help?