APFIVE Differential Equation for Tank Volume
Water flows into a tank at a constant rate of 5 gallons per minute, while water simultaneously flows out at a rate proportional to the square root of the volume of water in the tank. If $$V(t)$$ represents the volume of water in the tank at time $$t$$ (in minutes), which differential equation correctly models this situation?
A
$$\displaystyle\frac{dV}{dt} = 5 + k\sqrt{V}$$, where $$k > 0$$
B
$$\displaystyle\frac{dV}{dt} = 5 - kV$$, where $$k > 0$$
C
$$\displaystyle\frac{dV}{dt} = 5 - k\sqrt{V}$$, where $$k > 0$$
D
$$\displaystyle\frac{dV}{dt} = 5\sqrt{V} - k$$, where $$k > 0$$
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