Question

in a school with 1500 students , one student returned from vacation with a contagious flu virus on 1st January. the spread of the virus through student body is given by y=1500/1+1499e^-0.85t where y is the total number of students infected after t days. the school would cancel classes if 40% or more of the students are ill.
1) how many students would be infected after 6 days?
2)from which date onwards will the school have to cancel classes?

Answer 1

1) t=6
1500
2) January 6th = because January 1st is first day

Answer 2

I think you meant:

y = 1500/(1+1499e^-0.85t)

when t = 6 , I get
y = 148 , to the nearest whole number

40% of 1500 = 600

so 1500/(1+1499e^-0.85t) = 600
600(1+1499e^-0.85t) = 1500
1+1499e^-0.85t = 2.5
1499e^-0.85t = 1.5
e^-.85t = .001000667
-.85t = -6.907
t = 8.126

It would take 8 days to hit 400 students infected.