the increase in a persons body temperature (t(t)), above (98.6^{circ}f), can be modeled by the function…
the increase in a persons body temperature (t(t)), above (98.6^{circ}f), can be modeled by the function (t(t)=\frac{4t}{t^{2}+1}), where (t) represents time elapsed. what is the meaning of the horizontal asymptote for this function?\nthe horizontal asymptote of (y = 0) means that the persons temperature will approach (98.6^{circ}f) as time elapses.\nthe horizontal asymptote of (y = 0) means that the persons temperature will approach (0^{circ}f) as time elapses.\nthe horizontal asymptote of (y = 4) means that the persons temperature will approach (102.6^{circ}f) as time elapses.\nthe horizontal asymptote of (y = 4) means that the persons temperature will approach (4^{circ}f) as time elapses.
Answer
Brief Explanations:
First, find the horizontal - asymptote of the function $T(t)=\frac{4t}{t^{2}+1}$. As $t\to\pm\infty$, divide both numerator and denominator by $t^{2}$: $\lim_{t\to\pm\infty}\frac{4t}{t^{2}+1}=\lim_{t\to\pm\infty}\frac{\frac{4}{t}}{1 + \frac{1}{t^{2}}}=0$. The function $T(t)$ represents the increase in body - temperature above $98.6^{\circ}F$. So, when the horizontal asymptote is $y = 0$, it means the increase in temperature approaches $0^{\circ}F$ as time elapses, i.e., 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.