[tex]\bf \qquad \qquad \textit{inverse proportional variation}
\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
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\stackrel{\textit{\underline{s} ound intensity varies inversely as the square of the \underline{d}istance from source}}{s=\cfrac{k}{d^2}}[/tex]
so, let's say, you have an original distance of say "x" meters, namey d = x, and then you move away and change it to 9 times as much, namely d = 9x, let's check.
[tex]\bf \stackrel{\textit{original distance}}{s=\cfrac{k}{(x)^2}}\qquad \qquad \stackrel{\textit{new distance}}{s=\cfrac{k}{(9x)^2}}\implies s=\cfrac{k}{(9^2x^2)}\implies s=\cfrac{k}{81x^2}
\\\\\\
s=\cfrac{k}{x^2}\cdot \cfrac{1}{81}\impliedby \textit{notice, the new sound intensity is }\frac{1}{81}\textit{ of the original}[/tex]
