Find and interpret the horizontal asymptote

Question

a persons temperature T, in degrees Farenheit,during an illness is given by the function T(t) = 98.6t^2+ 4t + 98.6/ t^2+1 where time t is given in hours since then onset of the illness. Find and interpret the horizontal asymptote.

Answer 1

T(t) = (98.6t² + 4t + 98.6) / (t² + 1)

Notice that the order of both the numerator and denominator is 2.

So, the horizontal asymptote will be the ratio of the coeffecient of t².

Thus, the horizontal asymptote is

T = 98.6

When you graph this equation, you will see that it never crosses T = 98.6.

This means the person's temperature will never be below 98.6 degrees Farenheit.

*Please feel free to ask me any question for clarification.