A tank with a capacity of 1600 L is full of a mixture of water and chlorine with a concentration of 0.0125 g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 16 L/s. The mixture is kept stirred and is pumped out at a rate of 40 L/s. Find the amount of chlorine in the tank as a function of time. (Let *y* be the amount of chlorine in grams and *t* be the time in seconds.)

We are given a tank with an initial chlorine concentration of 0.0125 g/L in 1600 L of water. Fresh water is pumped into the tank at a rate of 16 L/s, and the mixture is pumped out at a rate of 40 L/s. The mixture is well-stirred, so the concentration of chlorine in the tank is uniform at all times.

We are tasked with finding the amount of chlorine \( y(t) \) in grams as a function of time \( t \) in seconds.

### Step 1: Setting up the differential equation

Let:
- \( y(t) \) represent the amount of chlorine (in grams) in the tank at time \( t \),
- The volume of water decreases at a rate of \( 40 - 16 = 24 \, \text{L/s} \), so after \( t \) seconds, the volume in

A tank with a capacity of 1600 L is full of a mixture of water and chlorine with a concentration of 0.0125 g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 16 L/s. The mixture is kept stirred and is pumped out at a rate of 40 L/s. Find the amount of chlorine in the tank as a function of time. (Let y be the amount of chlorine in grams and t be the time in seconds.)

Learn how to find the amount of chlorine in a 1600 L tank with a concentration of 0.0125 g/L, as fresh water is pumped in at 16 L/s and the mixture is pumped out at 40 L/s. This problem involves differential equations, mixture problems, and exponential decay concepts, suitable for first-year calculus students.

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