the increase in a persons body temperature ( t(t) ), above ( 98.6^{circ} mathrm{f} ), can be modeled by the…

the increase in a persons body temperature ( t(t) ), above ( 98.6^{circ} mathrm{f} ), can be modeled by the function ( t(t)=\frac{4 t}{t^{2}+1} ), where ( t ) represents time elapsed. what is the meaning of the horizontal asymptote for this function?\n- the horizontal asymptote of ( y = 0 ) means that the persons temperature will approach ( 98.6^{circ} mathrm{f} ) as time elapses.\n- the horizontal asymptote of ( y = 0 ) means that the persons temperature will approach ( 0^{circ} mathrm{f} ) as time elapses.\n- the horizontal asymptote of ( y = 4 ) means that the persons temperature will approach ( 102.6^{circ} mathrm{f} ) as time elapses.\n- the horizontal asymptote of ( y = 4 ) means that the persons temperature will approach ( 4^{circ} mathrm{f} ) as time elapses.

the increase in a persons body temperature ( t(t) ), above ( 98.6^{circ} mathrm{f} ), can be modeled by the function ( t(t)=\frac{4 t}{t^{2}+1} ), where ( t ) represents time elapsed. what is the meaning of the horizontal asymptote for this function?\n- the horizontal asymptote of ( y = 0 ) means that the persons temperature will approach ( 98.6^{circ} mathrm{f} ) as time elapses.\n- the horizontal asymptote of ( y = 0 ) means that the persons temperature will approach ( 0^{circ} mathrm{f} ) as time elapses.\n- the horizontal asymptote of ( y = 4 ) means that the persons temperature will approach ( 102.6^{circ} mathrm{f} ) as time elapses.\n- the horizontal asymptote of ( y = 4 ) means that the persons temperature will approach ( 4^{circ} mathrm{f} ) as time elapses.

Answer

Explanation:

Step1: Analyze the horizontal asymptote of (T(t)=\frac{4t}{t^{2}+1})

For a rational function (y = \frac{f(t)}{g(t)}) where (f(t)=4t) (degree (n = 1)) and (g(t)=t^{2}+1) (degree (m=2)). When (n<m), the horizontal asymptote is (y = 0).

Step2: Interpret the meaning of the horizontal asymptote in the context

Since (T(t)) represents the increase in body - temperature above (98.6^{\circ}F). As (t\rightarrow\infty), (T(t)\rightarrow0). So the person's temperature (original temperature (98.6^{\circ}F) plus (T(t))) will approach (98.6^{\circ}F) as (t\rightarrow\infty)

Answer:

The horizontal asymptote of (y = 0) means that the person’s temperature will approach (98.6^{\circ}F) as time elapses.