The number of students infected with the flu on a college campus after t days is modeled by the function $\mathrm { P } ( \mathrm { t } ) = \frac { 600 } { 1 + 39 \mathrm { e } ^ { - 0.3 \mathrm { t } } }$ When will the number of infected students be 300?
A) About 16 days
B) About 14 days
C) About 8 days
D) About 12 days

Question

Quizplus · Accepted Answer

To find when the number of infected students is 300, set $ P(t) = 300 $ and solve for $ t $:  $$ 300 = \frac{600}{1 + 39e^{-0.3t}} $$  $$ 1 + 39e^{-0.3t} = 2 $$  $$ 39e^{-0.3t} = 1 $$  $$ e^{-0.3t} = \frac{1}{39} $$  Taking the natural logarithm of both sides:  $$ -0.3t = \ln\left(\frac{1}{39}\right) $$  $$ t = -\frac{\ln\left(\frac{1}{39}\right)}{0.3} $$  Calculating this gives approximately 12 days.

The Number of Students Infected with the Flu on a College