Question

The equation y= -5.131x^2 + 31.821x - 3.333 approximates the number of people standing in line to catch a commuter train x hours after 5 am
what is the best estimate for the number of people in line at 7 a.m?
A.) 23
B.) 27
C.) 32
D.) 40

I'm trying to help my little sister, but i haven't done sophomore math in a couple of years so I'm not entirely sure, this is for a study guide for her finals so any help is really appreciated!

Answer 1

Alright! This question demands that we evaluate
$f(x) = - 5.131 {x}^{2} + 31.821x - 3.333$

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
$x = 2$
into the given function to obtain,



$f(2) = - 5.131 \times {2}^{2} + 31.821 \times 2 - 3.333$




$f(2) = - 5.131 \times 4 + 31.821 \times 2 - 3.333$
$f(2) = - 20.524+ 63.642 - 3.333$
$\Rightarrow f(2) = 39.785$
But we are dealing with number of people, and we cannot half fractional number of people.
Rounding to the nearest whole number gives,

$f(2) = 40 \: people$

This means that 2 hours 5am we have 40 people standing in the line to catch up the commuter train.

$The correct answer is option D.$

Answer 2

The answer should be D since after 5 am to 7 am only two hours have passed so x=2, and then you plug in the x as 2 and solve it. You might get not around answer like 39.785 but when you round it, it would be 40.