The increase in a person’s body temperature cap t times t , above 98.6 degrees F, can be modeled by the function cap t times t is equal to the fraction with numerator 4 t and denominator t squared plus 1 , where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?
Answer
A
The horizontal asymptote of y is equal to 4 means that the person’s temperature will approach 4 degrees F as time elapses.
B
The horizontal asymptote of y is equal to 0 means that the person’s temperature will approach 98.6 degrees F as time elapses.
C
The horizontal asymptote of y is equal to 0 means that the person’s temperature will approach 0 degrees F as time elapses.
D
The horizontal asymptote of y is equal to 4 means that the person’s temperature will approach 102.6 degrees F as time elapses.
Explanation
As time t gets larger, the function 4t/(t² + 1) approaches 0, so its horizontal asymptote is y = 0. This function represents the temperature increase above 98.6°F, not the total temperature. Therefore, the person’s temperature approaches 98.6°F as time elapses, which is choice C.
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