Question

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Explanation:

Find the horizontal asymptote

Using the Horizontal Asymptotes and Rational Functions knowledge points

$$ \lim_{t \to \infty} T(t) = \lim_{t \to \infty} \frac{4t}{t^2 + 1} = 0 $$

The horizontal asymptote is \(y = 0\).

Interpret the physical meaning

The function \(T(t)\) models the temperature increase above \(98.6^\circ\text{F}\).
As time \(t \to \infty\), the increase \(T(t) \to 0^\circ\text{F}\).
Therefore, the actual body temperature approaches \(98.6^\circ\text{F} + 0^\circ\text{F} = 98.6^\circ\text{F}\).

Answer:

• (A) The horizontal asymptote of \(y = 0\) means that the person's temperature will approach \(98.6^\circ\text{F}\) as time elapses. (Correct answer)
• (B) The horizontal asymptote of \(y = 0\) means that the person's temperature will approach \(0^\circ\text{F}\) as time elapses.
• (C) The horizontal asymptote of \(y = 4\) means that the person's temperature will approach \(102.6^\circ\text{F}\) as time elapses.
• (D) The horizontal asymptote of \(y = 4\) means that the person's temperature will approach \(4^\circ\text{F}\) as time elapses.