Find the amount of chlorine in the tank as a function of time?   A tank with a capacity of 4000 L is full of a mixture of water and chlorine with a concentration of 0.005g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 40 L/s. The mixture is kept stirred and is pumped out at a rate of 100 L/s.   (Let y be the amount of chlorine in grams and t be the time in seconds.)   Thank you.  

Expert Answers

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There is 20 grams (4000L*0.005g/L) of clorine in the tank at t=0.

The amount of clorine in the tank as a function of time is A(t).

The amount of water in the tank as a function of time is 4000-60t.

The concentration of clorine in the tank is `C(t)=A(t)/(4000-60t)` .

The amount of clorine leaving the tank as a function of time is

`100C(t)=(100A(t))/(4000-60t) `

So `A(t)=20-(100A(t))/(4000-60t)t`

So `A(t)+(100tA(t))/(4000-60t) = 20`

`A(t)(1+(100t)/(4000-60t))=A(t)(4000-60t+100t)/(4000-60t) = 20`

So our answer is

`A(t) = (20(4000-60t))/(4000+40t)`

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