First, I find it helpful to write the function myself.
There is a set fee of $120, and $5 per <em>n</em> badges.
<em />120 + 5<em>n
</em>
This is a basic model. Now we can see if any match.
f(n) = 5<em>n</em> + 120 matches.
Let me know if you found any errors.