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Problem 34 Easy Difficulty

A tank with a capacity of 400 L is full of a mixture of water and chlorine with a concentration of 0.05 g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 4 L/s. The mixture is kept stirred and is pumped out at a rate of 10 L/s. Find the amount of chlorine in the tank as a function of time.

Answer

$$
x=20\left(\frac{200-3 t}{200}\right)^{5 / 3}
$$

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Video Transcript

when you're talk to solve problem number 30 34 so we can let y t done it. Uh, you know the amount off hollerin in the tank at 20 in seconds. So why off zero equal or went? 05 Grandpa Leader, Multiply oy for 100 leaders equal 20 graham. So the amount off liquid in tank at Time T is 40 4 400 story minus six g Peter. So since for later off water enters the bank each second until later off liquid lives the tank h second. That's a concentration off calorie in at 90. Azaz concentration as equal. Um, see off t why g over for I want it one a 60 ground leader and coloring doesn't enter the thing, but it leaves at carry it off. Uh, all off t lives great Ill. Why off t over 460. Grumble later. Want deploy then leader per second So it will be equal then. Boy of G over 400 minus 60 round the second. Therefore do you? Why, bye DT um equal minus five. Why equal 20 100 minor, three t so by integration for both sides. Um sorry. Education for the off site so we can get that. Lynn. Why? Equal five, um, life over three. Lynn 20 100 minus Priti loss. See? So why equal exponential off? Five over three Lynn. 20 100 miners, three d plus C. So it will be equal E to the power. See? Multiply 2200 minus three. T to the power five over three. So now at, uh, why to equal 20 equal e off. See that, uh, that 200. So far. 5/3. So E off. See? Equal to any over 200. Multiple to the power 5/3. So why off T equal? Uh, 20 Multiple. Oy. 200 minus three G. The power five over three. Over 20 105 over three. Equal 20. Multiple. Oy. Um, sorry. Equal 20 multiplying one minus a 1.0, 15 t to the power five over. Three Them So that for tea? Less than 60. 66 uh, Thio over three on greater than people. At which time the tank is empty. Thanks for watching