Ans: (a) $y=\dfrac{972}{\sqrt{x}}$ (b) $27$
- Let $y = \dfrac{k}{\sqrt{x}}$, where $k$ is a non-zero constant.
When $x=144$, $y=81$. We have
$\begin{array}{rcl}
81 & = & \dfrac{k}{\sqrt{144}} \\
81 & = & \dfrac{k}{12} \\
k & = & 972
\end{array}$Therefore, $y = \dfrac{972}{\sqrt{x}}$.
- Sub. $x=324$ into the equation found in (a), we have
$\begin{array}{rcl}
y & = & \dfrac{972}{\sqrt{324}} \\
& = & 54
\end{array}$Hence, the change in the value of $y$
$\begin{array}{cl}
= & 81 – 54 \\
= & 27
\end{array}$
