Expert: Steve Holleran - 3/14/2007

Question
i need to find the function that works for each equation.
when n=10 c=20
when n=20 c=35
when n=30 c=50
when n=40 c=65
when n=50 c=80
what function can be used to find the answer for each of these?

Answer
Hi Tara,

Well, I'm going to assume a couple things here, since you don't give me too much info to go on :  I'm thinking this is a linear function, okay?


That means it can be written:   c = a*n + b

There are several ways to work it out.  One way is to find the slope of the line the function represents, which is also called the rate of change.  An easy way to do this is to notice that when n goes from 10 to 20, which is a change of 10, c goes from 20 to 35, a change of 15.  The rate of change of c with regard to n then is 15/10 or 1.5.

So now you know that variable "a" = 1.5 :

              c = 1.5 * n + b

To find b, just substitute any of the pairs of values given for c and n.  Let's say you choose 30 and 50:

              50 = 1.5 * 30 + b

              50 = 45 + b            so, b = 5

and the function is c = 1.5*n + 5

You can check the other pairs of values, and you'll see this function works fine.

I hope this helps you (and your little bro) out!

Steve Holleran