On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by , where y is the total number infected at time t (in days). The school will shut down if 50% of the students are ill. What value of t corresponds to this percentage?
A) Infinity
B) 8.19
C) 9.30
D) 6.44
E) 3.96

Question

On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by  , where y is the total number infected at time t (in days). The school will shut down if 50% of the students are ill. What value of t corresponds to this percentage? ​
A) Infinity 
B) 8.19 
C) 9.30 
D) 6.44 
E) 3.96

Quizplus · Accepted Answer

We need to find the value of t for which 50% of the students are infected, which means y = 0.5(10,000) = 5,000.

Substituting this value in the given equation, we get:

5,000 = 10,000 / (1 + e^(-0.25t))

Solving for t using logarithms, we get:

t = -4ln(1 - 0.5) / 0.25 = 9.30 days

Therefore, the answer is (C) 9.30.

On a College Campus of 10,000 Students, a Single Student