SOLUTION: An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days af

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Question 1124526: An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days after it broke out is given by the model
P = −t^2 + 17t + 180, where 1 ≤ t ≤ 6.
Find the day that 240 students had the flu. Recall that the restriction on t is at most 6.
t =
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
240=-t^2+17t+180
so t^2-17t+60=0
(t-12)(t-5)=0
t=5 days, since 12 days is not allowed.
graph%28300%2C300%2C-5%2C10%2C-20%2C280%2C-x%5E2%2B17x%2B180%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P+=+240+
+-t%5E2+%2B+17t+%2B+180+=+240+
+-+t%5E2+%2B+17t+-+60+=+0+
+%28+-t+%2B+12+%29%2A%28+t+-+5+%29+=+0+
+t+=+12+
+t+=+5+
The lower value is OK, +1+%3C=+t+%3C=+6+
On the 5th day 240students got the flu
Here’s the plot:
+graph%28+700%2C400%2C+-5%2C+30%2C+-30%2C+300%2C+-x%5E2+%2B+17x+%2B+180+%29+