Answer
≈ $5$ $ft/sec$
Work Step by Step
$\frac{dy}{dx}$ = $9e^{\frac{-x}{3}}(\frac{-1}{3})$ = $-3e^{\frac{-x}{3}}$
$\frac{dy}{dt}$ = $\frac{dy}{dx}$*$\frac{dx}{dt}$
$\frac{-1}{4}(\sqrt{9-y})$ = $(-3e^{\frac{-x}{3}})$$\frac{dx}{dt}$
$\frac{-1}{4}(\sqrt{9-9e^{\frac{-x}{3}}})$ = $(-3e^{\frac{-x}{3}})$$\frac{dx}{dt}$
$\frac{dx}{dt}$ = $\frac{1}{4}(\frac{(\sqrt{1-e^{\frac{-x}{3}}}}{e^{\frac{-x}{3}}})$
$\frac{dx}{dt}$$|_{{\,x=9}}^{{\,}}$ = $\frac{1}{4}(\frac{(\sqrt{1-e^{-3}}}{e^{-3}})$ ≈ $5$ $ft/sec$
