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 = −t2 + 17t + 140,
where
1 ≤ t ≤ 6.
Find the day that 170 students had the flu. Recall that the restriction on t is at most 6.