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.

Ona 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?

A. There are 92 people in the amusement park 4 hours after the gates open.

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

C. there are 692 people in the amusement park four hours after the gates open.

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

Answer 1

Explanation:

Answer 2

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

Explanation:

Rate at which people enter:

e(x)=0.03x^3 + 2

Rate at which people leave:

L(x)=0.5x + 1

Rate at which the number of people in the park is changing:

(e - L)(x) = 0.03x^3 + 2 - (0.5x + 1) = 0.03x^3 - 0.5x + 1

4 hours after the gates open, the rate is:

(e - L)(4) = 0.03(4)^3 - 0.5(4) + 1 = 0.92 hundreds of people per hour or 0.92*100 = 92 people per hour