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?
Answers
Answer:
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.
The domain of the function should be [tex]0\leq n\leq m[/tex] 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,
[tex]f(x)=30n[/tex]
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 [tex]0\leq n\leq m[/tex] where n and m are integers because they represent the number of people.
For more details, refer to the link:
https://brainly.com/question/15099991
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