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Differential Calculus:

Question 1: A container contains 0.5 kg of sugar dissolved in 20 L of liquid. If water flows in the rate of 0.2 L/min and the liquid sugar solution flows out at the same rate. What is the concentration of sugar after 10 min?

Solution: We know that the amount of liquid in the container stays constant, so we only need to concentrate on the amount of sugar inside the container. If we take out 0.2L of sugar water from a well-mixed salt solution of 20L, then we are taking out 0.2/20 = 0.01 portion of sugar/min. So, the rate of change of the amount of sugar, dS/dt = -0.01S, with initial condition S(0) = 0.5.

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