a hotel charges $75 each night for the first two nights and $50 for each additional nights stay.

Question

I need to write a piecewise function to represent the cost for staying at the hotel and i have no idea how to do it.

Answer 1

Let n be the number of nights spent.

 

Since the first two nights are each $75, if n≤2, the $75n

 

Since each additional night after that, is $50, if n>2, such a client pays $150 for the first 2 nights and $50 for each of the other n-2 nights for a total of $[150+50(n-2)] = $(50n+50)

 

So the function for the cost is

 

C(n) = 75n for n ≤ 2

C(n) = 50n+50 for n > 2

 

I'm not sure why you added trigonometry as the topic for this question.