One Model for the Spread of an Epidemic Is That $40 \%$

Multiple Choice

One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of 3,000 inhabitants, 120 people have a disease at the beginning of the week and 1,600 have it at the end of the week. How long does it take for $40 \%$ of the population to be infected?
Select the correct answer.

A) 25 days
B) 20 days
C) 5 days
D) 35 days
E) 15 days