Alright! This question demands that we evaluate
[tex]f(x) = - 5.131 {x}^{2} + 31.821x - 3.333[/tex]
at a given value of x, which was not given directly. But enough information was given to help us determine that value of x.
After 5am, 7am is a two our interval. So we plug in
[tex]x = 2 [/tex]
into the given function to obtain,
[tex]f(2) = - 5.131 \times {2}^{2} + 31.821 \times 2 - 3.333[/tex]
[tex]f(2) = - 5.131 \times 4 + 31.821 \times 2 - 3.333[/tex]
[tex]f(2) = - 20.524+ 63.642 - 3.333[/tex]
[tex]\Rightarrow f(2) = 39.785[/tex]
But we are dealing with number of people, and we cannot half fractional number of people.
Rounding to the nearest whole number gives,
[tex]f(2) = 40 \: people[/tex]
This means that 2 hours 5am we have 40 people standing in the line to catch up the commuter train.
[tex]<b>The correct answer is option D.</b>[/tex]
