The rate of change of the volume, \(V\), of water in a tank with respect to time, \(t\), is directly proportional to the square root of the volume. Which of the following is a differential equation that describes this relationship.

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Direct variation can be modeled with the equation \(y=kx\) for two variables \(x\) and \(y\).

Since the rate of change of the volume with respect to time \(\dfrac{dV}{dt}\) is directly proportional to the square root of the volume \(\sqrt{V}\),

$$ y=kx $$ $$ \boxed{\frac{dV}{dt}=k\sqrt{V}} $$