Pre-Calc multiple choice...someone help?

Question

The number of students infected with the flu on a college campus after t days is modeled by the function P(t)= 200/1 + 39e^-0.3t

When will the number of infected students be100?

A) About 16 days
B) About 12 days
C) About 14 days
D) About 8 days

Answer 1

100 = 200 / (1+ 39e^-0.3t)
2 = 1+ 39e^-0.3t
1 = 39e^-0.3t
(1/39) = e^-0.3t
ln(1/39) = -0.3t
ln(1/39) / -0.3 = t
t = 12.21

... so B is the best estimate.

Answer 2

The number of students infected with the flu on a college campus after t days is modeled by the function
P(t)= 200/1 + 39e^-0.3t

When will the number of infected students be100?
________

I assume you mean

P(t)= 200 / [1 + 39e^(-0.3t)]

100 = 200 / [1 + 39e^(-0.3t)]
1 = 2 / [1 + 39e^(-0.3t)]
1 + 39e^(-0.3t) = 2
39e^(-0.3t) = 1
e^(-0.3t) = 1/39

ln[e^(-0.3t)] = ln(1/39)
-0.3t = -ln(39)
0.3t = ln(39)
t = ln(39) / 0.3 ≈ 12.21 days

The answer is B.