the increase in a persons body temperature T(t), above 98.6 degrees F, can be modeled by function T(t)=4t/t^2+1, t represents the time elapsed. what is the meaning of the horizontal asymptote for this function

The horizontal asymptote is the limit of the temperature as time goes to infinity.

If we ignore the constant in the denominator, then
[tex]T = \frac{4t}{t^2} = \frac{4}{t} [/tex]

And the limit as t-> infinity is 0
[tex] \lim_{t \to \infty} \frac{4}{t} = 0 [/tex]

This means the temperature will decrease over time approaching 98.6 in the long run.