Question

The equation ​ yˆ=−5.131x2+31.821x−3.333 ​ approximates the number of people standing in line to catch a commuter train x hours after 5 a.m.

What is the best estimate for the number of people in line at 9 a.m.?



32

40

42 (THIS IS THE ANSWER)

46

Answer 1

From 5 a.m to 9 a.m there 4 hours. x=4
y=5.131x² + 31.821x - 3.333
y=5.131 (4²) + 31.821 (4) - 3.333
y= 41.855

Approximately 42 people

Answer 2

The best estimate for the number of people in line at 9 a.m is 42.

Explanation

Given x is number of people standing in line to catch a commuter train x hours after 5 a.m

Number of hours from 5 a.m to 9a.m= 4 hours.

Plugging x=4 in the given equation we have:

`y=-5.1314^(2) +31.821(4)-3.333`

Or ,

y=-5.1314(16)+127.284-3.333

y=-82.1024 +127.284-3.333

y=41.84

Or y=42 .