Expert: Steve Holleran - 12/15/2007

Question
tim finds that if his vacation is 9 days long it will cost him $3111 and if it is 23
days long it will cost him $5547.  

how can i express the total cost (C) of the vacation as a function of the number
of days of his vacation (n).

Answer
Hi Jon,


Okay, there are several ways to deal with this.  One nice way is to consider the information as ordered pairs, just like points in the (x,y) plane.  Here, our ordered pairs will be called (n, C).

So, the two pairs are :

A(9 , 3111) and B(23 , 5547)

We want an equation in the form C = m * n + b .

Well, the slope, m, is m = (5547 - 3111) / (23 - 9)

                      m = 2436/14 = 174

So now you have C = 174 * n + b.  Okay, then lets substitute the first (n, C) point:

             3111 = 174 * 9 + b

             3111 = 1566 + b     so b = 1545

and so your function is C =  174n + 1545

Hope this helps.

Steve