Question

A movie theater seats 500 people. For any particular show, the amount of money the theater makes is a function, m(n), of the number of people, n, in attendance. If a ticket costs $6, find the domain and range of this function.

Answer 1

Given a theater has 500 seats. and a ticket costs 6$.

Let n be the number of people who bought tickets.

Then income , m(n) = 6*n

Now we need to find domain and range of above function.

Since n is number of people, it cannot be negative and theater can maximum seat 500 people that is n must be less than or equal to 500.

Hence domain is [0,500].

And minimum income will be when no tickets sold that is $0.

And maximum income will be when maximum tickets sold that is 500*6 = 3000$

Hence range is [0, 3000]