Question

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? the horizontal asymptote of (y = 0) means that the persons temperature will approach (98.6^{circ}f) as time elapses. the horizontal asymptote of (y = 0) means that the persons temperature will approach (0^{circ}f) as time elapses. the horizontal asymptote of (y = 4) means that the persons temperature will approach (102.6^{circ}f) as time elapses. the horizontal asymptote of (y = 4) means that the persons temperature will approach (4^{circ}f) as time elapses. the horizontal asymptote of (y = 4) means that the persons temperature will approach (4^{circ}f) as time elapses.

Explanation:

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 limit as $t\to\infty$. Using the rule for limits of rational functions where the degree of the denominator is greater than the degree of the numerator, $\lim_{t\to\infty}\frac{4t}{t^{2}+1}=0$. 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.