Algebra choice question

Question

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 the 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?

(A) The rate at which the number of people in the park is changing 4 hours after the gates open is 92 people per hour.

(B)There are 92 people in the amusement park 4 hours after the gates open.

(C)The rate at which the number of people in the park is changing 4 hours after the gates open is 692 people per hour.

(D)There are 692 people in the amusement park 4 hours after the gates open.

Answer 1

To answer, you'll need to substitute x = 4 into each of the functions and subtract, as they're looking for the difference between the rate of people entering and rate leaving. x is the time elapsed since the gates opened.

The first function yields a value of 3.92 hundred people/hr entering 4 hrs after the gates opened; the 2nd functions has a value of 3.00 hundred people/hr leaving 4 hrs after opening. The difference is a net of 92/hr entering. The best answer is A.