Question

the equation y= - 5.131x2+ 31.821x - 3.333 approximates the number of people standing in line to catch a commuter train x hours after 5a.m. , what is the best estimate for the number of people in line at 7 a.m.? A. 23 B.27 C.32 D.40

Answer 1

We are given function: y= $- 5.131x^2+ 31.821x - 3.333$

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 $y=- 5.131x^2+ 31.821x - 3.333$, we get

$y=- 5.131(2)^2+ 31.821(2) - 3.333$

Let us simplify it now.

2^2= 4.

Therefore,

$y=- 5.131(4)+ 31.821(2) - 3.333$

= -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.