So I have:
10 100
40 6
70 2
100 1
That is inverse square correct?
Now, how would I 'model that using the correct inverse proportion' and find the value of k using 10 100
An inverse proportion is of the form y= k/x or xy= k. If that were correct we would have k= 10(100)= 1000 but 40(6)= 240, not 1000. If it were $\displaystyle y= k/x^2$ or $\displaystyle x^2y= k$ then, depending on which number is x, we have either [tex]k= (10)(100^2)= 100000[tex] or $\displaystyle k= (10^2)(100)= 10000$. In the first case, $\displaystyle (40)(6^2)= 1440$, which is not right, and in the second, $\displaystyle (40^2)(6)= 9600$, also not right. So it is not "inverse square". If you were to try a generic $\displaystyle y^n= k/x^m$ or $\displaystyle x^my^n= k$, we could write $\displaystyle (10^m)(100^n)= k$ and $\displaystyle (40^m)(6^n)= k$. Dividing one equation by the other [tex]\left(\frac{10}{40}\right)^m\left(\frac{100}{6}\ri ght)^n= 1[tex] or $\displaystyle \left(\frac{1}{4}\right)^m\left(\frac{50}{3}\right )^n$. Especially easy is the last pair: $\displaystyle (100^m)(1^n)= 100^m= k$ so that $\displaystyle \left(\frac{100}{10}\right)^m\left(\frac{1}{100}\r ight)^n= 1$. That gives you two equations to solve for m and n.