## College Algebra (10th Edition)

$\color{blue}{t=\dfrac{12}{\sqrt{x}}}$
$y$ varies inversely with $\sqrt{x}$, so the equation that represents the variation is: $y=\dfrac{k}{\sqrt{x}}$ Since $y=4$ when $x=9$, substituting these into the tentative equation above gives: $y=\dfrac{k}{\sqrt{x}} \\4=\dfrac{k}{\sqrt{9}} \\4=\dfrac{k}{3} \\3(4) = \dfrac{k}{3} \cdot 3 \\12=k$ Thus, the equation of the inverse variation is: $\color{blue}{t=\dfrac{12}{\sqrt{x}}}$