the increase in a persons body temperature t(t), above 98.6°f, can be modeled by the function t(t) = 4t /…

the increase in a persons body temperature t(t), above 98.6°f, can be modeled by the function t(t) = 4t / (t² + 1), 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 persons temperature will approach 98.6°f as time elapses. the horizontal asymptote of y = 0 means that the persons temperature will approach 98.6°f as time elapses. the horizontal asymptote of y = 0 means that the persons temperature will approach 0°f as time elapses. the horizontal asymptote of y = 4 means that the persons temperature will approach 102.6°f as time elapses. the horizontal asymptote of y = 4 means that the persons temperature will approach 4°f as time elapses.

the increase in a persons body temperature t(t), above 98.6°f, can be modeled by the function t(t) = 4t / (t² + 1), 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 persons temperature will approach 98.6°f as time elapses. the horizontal asymptote of y = 0 means that the persons temperature will approach 98.6°f as time elapses. the horizontal asymptote of y = 0 means that the persons temperature will approach 0°f as time elapses. the horizontal asymptote of y = 4 means that the persons temperature will approach 102.6°f as time elapses. the horizontal asymptote of y = 4 means that the persons temperature will approach 4°f as time elapses.

Answer

Brief Explanations:

The function $T(t)=\frac{4t}{t^{2}+1}$ gives the increase in body - temperature above 98.6°F. To find the horizontal asymptote, we consider the behavior of the function as $t\to\pm\infty$. For a rational function $\frac{f(t)}{g(t)}$ where the degree of $g(t)$ is greater than the degree of $f(t)$ (here, degree of $f(t) = 1$ and degree of $g(t)=2$), the horizontal asymptote is $y = 0$. This means the increase in temperature above 98.6°F approaches 0 as time elapses, so the person's temperature approaches 98.6°F.

Answer:

The horizontal asymptote of $y = 0$ means that the person's temperature will approach 98.6°F as time elapses.