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 solve the equation 11eb0d3b_981b_00ae_9790_67c21da46e03_TB1243_11 = 0.5(10,000) = 5000.

Plugging in y=1 and solving for t, we get:

1 = 5000/(1+9999e^(-0.078t))

1 + 9999e^(-0.078t) = 5000

9999e^(-0.078t) = 4999

e^(-0.078t) = 4999/9999

t = -ln(4999/9999)/0.078

t ≈ 9.30

Therefore, the answer is (C) 9.30.

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