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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.
Feb 6, 2018
edited by adore.nuk  Feb 6, 2018

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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

Feb 6, 2018