Question

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? o the horizontal asymptote of y = 0 means that the persons temperature will approach 98.6°f as time elapses. o the horizontal asymptote of y = 0 means that the persons temperature will approach 0°f as time elapses. o the horizontal asymptote of y = 4 means that the persons temperature will approach 102.6°f as time elapses.

Explanation:

The horizontal asymptote of a function represents the value that the function approaches as the independent - variable (in this case time \(t\)) goes to positive or negative infinity. For the function \(T(t)=\frac{4t}{t + 1}\), we can find the horizontal asymptote by looking at the behavior of the function as \(t\to\infty\). Dividing both the numerator and denominator by \(t\), we get \(T(t)=\frac{4}{1+\frac{1}{t}}\). As \(t\to\infty\), \(\frac{1}{t}\to0\), so \(T(t)\to4\). This means that as time elapses, the person's temperature will approach \(98.6 + 4=102.6^{\circ}F\) since \(T(t)\) represents the increase in temperature above \(98.6^{\circ}F\).

Answer:

The horizontal asymptote of \(y = 4\) means that the person's temperature will approach \(102.6^{\circ}F\) as time elapses.