this function would count the profit of a month. To get the profit of longer periods you would need to do something like this:
[text]g(t) = t * f(n)[/text] where t is time.
I constructed the first function by simply looking at how much would one dog give profit. Since the fee is 500 and 200 of it is going to be spent away, 300 is left. So, profit from one dog is 300 dollars. However, if they don't have enough dogs, the doggy daycare company would get in debt because of 2000 dollars that it needs a month to operate, that's why I subtracted 2000 from the profit.