Determining quadratic function of this word problem

Question

I have this word problem in my homework:

A tour company offers back country hiking excursions at $160 per person for
groups up to 50. For groups larger than 50, the company will reduce the cost of 
every ticket by $2 for each person in excess of 50. What size of group would
produce the greatest revenue?

I'm not worried about finding out what the size of the group is that produces the greatest revenue. What I want to know is what the equation for this is. I was able to figure out this equation:

$$f(x) \ = \ 160x - 2(x-50) \ , $$

where $ \ x \ $ is the number of people and $ \ f(x) \ $ is the revenue. But that's a linear function and we're doing quadratic functions. So, There should be an exponent and I'm thinking there's more to this question than I see? Or is it a linear function?

Answer 1

Note that if you have $n > 50$ people, your revenue will be ticket price for each person (which is $160-2(n-50)$) times the number of people $n$, i.e. $(160-2(n-50))n$.