Setting Up a Differential Equation

Calculus Level 1

Suppose a pipe containing water with $0.2\text{ kg}$ of sugar per liter (l) runs into a tank filled with 400 l of water currently containing $10\text{ kg}$ of sugar. Furthermore, the flow from the pipe enters the tank at 10 l/min while at the same time a pipe drains the tank at the same rate. Set up the differential equation that models the amount of sugar in the tank.

\frac{dA}{dt}=40-\frac{A}{2}

\frac{dA}{dt}=2-\frac{A}{40}

\frac{dA}{dt}=2+\frac{A}{40}

\frac{dA}{dt}=40+\frac{A}{2}