A football stadium is capable of seating a maximum of m fans. For each game, the amount of money that the stadium brings in as revenue is a function of the number of
people, n, in attendance. If each ticket costs $30.00, what is the domain of this function?

The domain of the function should be where n and m are integers because they represent the number of people.

Given information:

A football stadium is capable of seating a maximum of m fans.

People attending the game are n.

The cost of each ticket is $30.

The  amount of money that the stadium brings in as revenue is a function of the number of  people, n.

So, the money will be calculated based on the attendance of people which implies that n will be the independent variable of the function.

So, the revenue generated can be written as,

Here, the value of n represents the domain of the function.

Now, the maximum number of people allowed in the stadium is m as there are only m seats.

Therefore, the domain of the function should be where n and m are integers because they represent the number of people.

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The revenue depends on the number of people n that purchases tickets, knowing that each ticket costs $30.00, the total revenue will be:

f(n) = $30.00*n

Now, we also know that the stadium is capable of seating a maximum of m fans, so the maximum possible value for n is m.

Now, for the function f(n), we have that:

The domain is the set of the possible values of n

The range is the set of the possible values of f(n).

We want to find the domain.

First, the minimum possible value of n is 0, the case where nobody purchases a ticket.

The maximum possible value of n is m, this is the case where the stadium is full.

Then the domain will be:

D= {n,m ∈ Z, 0 ≤ n ≤ m}

Where we imposed that n must be an integer number because n represents a whole quantity.

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