Question

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

Answer 1

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

If we ignore the constant in the denominator, then

`T = (4t)/(t^2) = (4)/(t)`

And the limit as t-> infinity is 0

`\lim_(t \to \infty) (4)/(t) = 0`

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

Answer 2

That the temperature of the person's body will always be above 98.6 degrees F

Explanation:

The function does not model the body temperature of the person, it models the change/increase in the body temperature. The fact that in the positive part of the t axis, which is where our focus is since time elapsed is always positive, never touches the t-axis but tends towards it from above meaning the change in temperature of the person's body is always positive no matter how much time elapses and is never zero which can be understood as meaning that the temperature of the person's body will always be above 98.6 degrees F