# Finding formula for a function

• Aug 24th 2009, 08:43 PM
JAMESveeder
Finding formula for a function
I need to find the formula for this function, and i'm not sure what to do...

Code:

x    f(x) -2    -25.22 0      3.50 2      32.22 4      60.94 6      89.66
I've looked all over the internet and can't find anything to help me out :(
• Aug 24th 2009, 08:48 PM
Chris L T521
Quote:

Originally Posted by JAMESveeder
I need to find the formula for this function, and i'm not sure what to do...

Code:

x    f(x) -2    -25.22 0      3.50 2      32.22 4      60.94 6      89.66
I've looked all over the internet and can't find anything to help me out :(

We can model the function using a linear equation.

Note that when x increases by 2, f(x) increases by 28.72

Since $f(0)=3.5=b$ and the slope of the line is $m=\frac{28.72}{2}=14.36$, it follows that the equation of the line is $f(x)=mx+b=14.36x+3.50$.
• Aug 24th 2009, 08:49 PM
CaptainBlack
Quote:

Originally Posted by JAMESveeder
I need to find the formula for this function, and i'm not sure what to do...

Code:

x    f(x) -2    -25.22 0      3.50 2      32.22 4      60.94 6      89.66
I've looked all over the internet and can't find anything to help me out :(

Try plotting it!

It's a straight line passing through (0,3.5) and with slope 14.36

CB
• Aug 24th 2009, 09:12 PM
JAMESveeder
Great explanation, thank you!

You can't use the same method for an exponential function though, can you?
• Aug 24th 2009, 09:19 PM
Prove It
Quote:

Originally Posted by JAMESveeder
Great explanation, thank you!

You can't use the same method for an exponential function though, can you?

No. For an exponential function, you would need to find a common RATIO. In other words, you need to find what each number is MULTIPLIED by to get the next.
• Aug 24th 2009, 09:33 PM
JAMESveeder
So with this:
Code:

x      g(x) .5    -1 1      0 2      1 4      1 8      3
Each number is multiplied by 2

So how would I apply that to the explanation that was said before?
• Aug 24th 2009, 10:23 PM
CaptainBlack
Quote:

Originally Posted by JAMESveeder
So with this:
Code:

x      g(x) .5    -1 1      0 2      1 4      2 8      3
Each number is multiplied by 2

So how would I apply that to the explanation that was said before?

you would find the line through the data: $x,\ \log_2(g(x))$ .. or on second thoughts $\log_2(x),\ g(x)$

CB
• Aug 24th 2009, 10:32 PM
JAMESveeder
Ah, thanks CaptainBlack :)

This helps a lot, thanks very much guys.