Question

The revenue from selling movie tickets is given by the function R(t) = 10t, where "t" is the number of tickets sold. The theater holds a maximum of 200 people. The profit is a function of the revenue "R" and is given by the function P(R) = 0.20R. What is the domain of the profit function P(R)?

Answer 1

Answer:

The domain of the profit function P(R) is

D = {R|R∈W|0≤R≤2000}

Step-by-step explanation:

Find the highest and lowest R values for R(t).

R(t) = 10t

Since the maximum number of people is 200, t ≤ 200.

You can't have a negative number of people, so t ≥ 0.

Sub t for 0

R(t) = 10t

R(0) = 10(0)

R(0) = 0

(0,0)

Sub t for 200

R(t) = 10t

R(200) = 10(200)

R(200) = 2000

In R(t), 0 ≤ R and R ≤ 2000.

In R(t), Range = {R|R∈W|0≤R≤2000}

Use 0 ≤ R ≤ 2000 to find the domain of P(R).

The domain in P(R) is the possible values of R because it's in the brackets.

We already know the possible values of R.

Domain = {R|R∈W|0≤R≤2000}

It sets the variable for domain, states the type of numbers R includes, and the specific numbers.

Whole numbers are numbers that are not partials starting from 0.

If you wanted to find the range of P(R), you would substitute R for 0 and 2000 in the equation to calculate the highest and lowest numbers of P.