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 or then, depending on which number is x, we have either [tex]k= (10)(100^2)= 100000[tex] or . In the first case, , which is not right, and in the second, , also not right. So it is not "inverse square". If you were to try a generic or , we could write and . Dividing one equation by the other [tex]\left(\frac{10}{40}\right)^m\left(\frac{100}{6}\ri ght)^n= 1[tex] or . Especially easy is the last pair: so that . That gives you two equations to solve for m and n.