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 + 13t + 150,
where
1 ≤ t ≤ 6.
Find the day that 180 students had the flu. Recall that the restriction on t is at most 6.
t = ?

Question

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 + 13t + 150,
 where 
1 ≤ t ≤ 6.
 Find the day that 180 students had the flu. Recall that the restriction on t is at most 6. 
t =  ?

emmynimmy · Answer

The cost function for a certain company is 
C = 40x + 800
 and the revenue is given by 
R = 100x − 0.5x^2.
 Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $800.