A tank initially contains 100 L of pure water

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

A tank initially contains 100 L of pure water. Brine containing 2 g/L of salt flows into the tank at 5 L/min, and the well-stirred mixture flows out at the same rate. Let S(t)S(t) denote the amount of salt (in grams) in the tank after tt minutes. Which expression gives S(t)S(t)? (a) 200e−0.05t200e^{-0.05 t} (b) 200+200e−0.05t200+200e^{-0.05 t} (c) 200(1−e−0.05t)200\bigl(1-e^{-0.05 t}\bigr) (d) 200(1−e−0.2t)200\bigl(1-e^{-0.2 t}\bigr)

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