We are given function: y= [tex]- 5.131x^2+ 31.821x - 3.333[/tex]
Where, x is the number of hours after 5a.m.
We need to approximates the number of people standing in line to catch a commuter train at 7 a.m.
From 5 a.m. to 7 a.m. total number of hours = 7-5 = 2 hours.
So, we need to plug x=2 in the given function.
Plugging x=2 in [tex]y=- 5.131x^2+ 31.821x - 3.333[/tex], we get
[tex]y=- 5.131(2)^2+ 31.821(2) - 3.333[/tex]
Let us simplify it now.
2^2= 4.
Therefore,
[tex]y=- 5.131(4)+ 31.821(2) - 3.333[/tex]
= -20.524 + 63.642 - 3.333.
= 39.785 or 40 approximately.
Therefore, the number of people in line at 7 a.m. is approximately 40 people.
Option D.40 is correct option.
