MATH SOLVE

5 months ago

Q:
# the increase in a persons body temperature T(t), above 98.6 degrees F, can be modeled by function T(t)=4t/t^2+1, t represents the time elapsed. what is the meaning of the horizontal asymptote for this function

Accepted Solution

A:

The horizontal asymptote is the limit of the temperature as time goes to infinity.

If we ignore the constant in the denominator, then

[tex]T = \frac{4t}{t^2} = \frac{4}{t} [/tex]

And the limit as t-> infinity is 0

[tex] \lim_{t \to \infty} \frac{4}{t} = 0 [/tex]

This means the temperature will decrease over time approaching 98.6 in the long run.

If we ignore the constant in the denominator, then

[tex]T = \frac{4t}{t^2} = \frac{4}{t} [/tex]

And the limit as t-> infinity is 0

[tex] \lim_{t \to \infty} \frac{4}{t} = 0 [/tex]

This means the temperature will decrease over time approaching 98.6 in the long run.