The original post is asking for a quantitative relationship, not a series of examples. There is nothing wrong about the basic guide number relationships used in the above answers, but the quantitative relationship between Guide Number and ISO is

the square root of (ISO/100).

In keeping with the use of a series of examples:

the square root of (200/100) is 1.4
the square root of (400/100) is 2
the square root of (800/100) is 2.8, etc.

The original asker may have wanted this quantitative relationship because his/her camera has ISO values other than 100, 200, 400, 800 etc.

There is a derivation of this relationship at:

http://www.discoverypark.info/effective_guide_number.htm

The original post is asking for a quantitative relationship, not a series of examples. There is nothing wrong about the basic guide number relationships used in the above answers, but the quantitative relationship between Guide Number and ISO is

$$ GN \propto \sqrt{\text{ISO}\over 100}\,.$$

In keeping with the use of a series of examples:

$$\begin{align} \sqrt{200\,/100} &= 1.4 \\ \sqrt{400\,/100} &= 2 \\ \sqrt{800\,/100} &= 2.8 \\ & \dots \end{align}$$

The original asker may have wanted this quantitative relationship because his/her camera has ISO values other than 100, 200, 400, 800 etc.

There is a derivation of this relationship at:

http://www.discoverypark.info/effective_guide_number.htm