Question

The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function T (t) = StartFraction 4 t Over t squared + 1 EndFraction, where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?
The horizontal asymptote of y = 0 means that the person’s temperature will approach 98.6ºF as time elapses.
The horizontal asymptote of y = 0 means that the person’s temperature will approach 0ºF as time elapses.
The horizontal asymptote of y = 4 means that the person’s temperature will approach 102.6ºF as time elapses.
The horizontal asymptote of y = 4 means that the person’s temperature will approach 4ºF as time elapses.

Answer 1

The first choice. As t → ∞, 4t/(t^2+1) → 0, so the temperature increase above 98.6°F goes to 0 — the person’s temperature approaches 98.6°F.