APFIVE Differential Equation for Tank Volume
Water enters a tank at a constant rate of 5 gallons per minute. Simultaneously, water is removed at a rate proportional to the square root of the volume of water in the tank. Let $$V(t)$$ be the volume of water in the tank at time $$t$$. Which of the following differential equations 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
$$\displaystyle\frac{dV}{dt} = 5\sqrt{V} - k$$, where $$k > 0$$
D
$$\displaystyle\frac{dV}{dt} = 5 + k\sqrt{V}$$, where $$k > 0$$
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