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 amusement park is modeled by the function
e(x) = 0.03x3 + 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?

Answer 1

Answer:

Maybe how many people are in the park

Answer 2

For given situation, (e - l)(4) means, there are 92 people in the amusement park 4 hours after the gates open.

What is a function?

"It is an expression that defines a relationship between one variable and another variable."

For given example,

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.

First we find the subtraction of functions $(e-l)(x)$.

$\Rightarrow (e-l)(x)=e(x)-l(x)\\\\\Rightarrow (e-l)(x)=0.03x^3 + 2-(0.5x + 1)\\\\\Rightarrow (e-l)(x)=0.03x^3+2-0.5x-1\\\\\Rightarrow (e-l)(x)=0.03x^3-0.5x+1$

For x = 4,

$\Rightarrow (e-l)(4)=0.03(4)^3-0.5(4)+1\\\\\Rightarrow \bold{(e-l)(4)=0.92}$

As, the rate is measured in hundreds of people per hour

So, (e - l)(4) means, there are 92 people in the amusement park 4 hours after the gates open.

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