The number of students infected with the flu on a college campus after t days is modeled by the function $P ( t ) = \frac { 360 } { 1 + 39 e ^ { - 0.3 t } }$ What is the maximum number of infected students possible?
A) 720 students
B) 360 students
C) 180 students
D) 9 students

Question

Quizplus · Accepted Answer

The maximum number of infected students possible is the horizontal asymptote of the function $P(t) = \frac{360}{1 + 39e^{-0.3t}}$, which occurs as $t$ approaches infinity. As $t$ goes to infinity, $e^{-0.3t}$ approaches 0, making the denominator approach 1. Thus, the maximum value of $P(t)$ is $360$, corresponding to option B.

The Number of Students Infected with the Flu on a College