A 50-L tank initially contains 4 g of salt dissolved in water

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A 50-L tank initially contains 4 g of salt dissolved in water. Brine with a concentration of 0.5 g/L flows into the tank at 3 L/min, and the well-stirred mixture flows out at the same rate so that the volume remains constant. Which differential equation best models the rate of change dQdt\dfrac{dQ}{dt} of the amount of salt Q(t)Q(t) (in grams) in the tank? (a) 1.5−Q501.5-\dfrac{Q}{50} (b) −1.5+3Q50-1.5+\dfrac{3Q}{50} (c) 1.5−3Q501.5-\dfrac{3Q}{50} (d) 0.5−3Q500.5-\dfrac{3Q}{50}

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