The gates of an amusement park are closely monitored to determine whether the number of people in the amusement park ever poses a safety hazard.

On a certain day, the rate at which people enter amusement park is modeled by the function e(x)=0.03x^3+2 where the rate is measured in hundreds of people per hour since the gates opened. The rate at which people leave the amusement park is modeled by the function l(x)=0.5x+1 , where the rate is measured in hundreds of people per hour since the gates opened.

What does (e−l)(4) mean in this situation?

- The rate at which the number of people in the park is changing 4 hours after the gates open is 692 people per hour.
- There are 92 people in the amusement park 4 hours after the gates open.
- The rate at which the number of people in the park is changing 4 hours after the gates open is 92 people per hour.
- There are 692 people in the amusement park 4 hours after the gates open.

adore.nuk
Feb 6, 2018

#1**+2 **

Hard to read these functions, but I think we have

e(x) = .03x^3 + 2

l (x) = .5x + 1

So .. ( e - l) = [ .03x^3 + 2 ] - [ .5x + 1 ] = .03x^3 - .5x + 1

So

(e - l ) (4) = .03(4)^3 - .5(4) + 1 = .92 ...this is in hundreds, so it converts to 92 people

So....this means that 4 hours after the park opens, the rate that the number of people is changing is 92 people per hour

CPhill
Feb 6, 2018