the increase in a persons body - temperature ...

# Explanation: ## Step1: Recall horizontal - asymptote concept For a rational function $y = \frac{f(t)}{g(t)}$ where $f(t)$ and $g(t)$ are polynomials, if the degree of $f(t)$ is less than the degree of $g(t)$, the horizontal asymptote is $y = 0$. For the function $T(t)=\frac{4t}{t^{2}+1}$, as $t\to\pm\infty$, we use the fact that for large $t$, the highest - degree terms dominate. Dividing both numerator and denominator by $t^{2}$, we get $T(t)=\frac{\frac{4}{t}}{1 + \frac{1}{t^{2}}}$. As $t\to\pm\infty$, $\frac{4}{t}\to0$ and $\frac{1}{t^{2}}\to0$, so the horizontal asymptote is $y = 0$. ## Step2: Interpret in context The function $T(t)$ represents the increase in a person's body temperature above $98.6^{\circ}F$. So when the horizontal asymptote of $T(t)$ is $y = 0$, it means that the increase in body temperature above $98.6^{\circ}F$ approaches $0$ as time elapses. In other words, the person's temperature will approach $98.6^{\circ}F$ as time elapses. # Answer: The horizontal asymptote of $y = 0$ means that the person's temperature will approach $98.6^{\circ}F$ as time elapses.