Need Help Setting up Differential Equation

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SUMMARY

The discussion focuses on modeling a contaminant's concentration in a tank using a differential equation. The tank initially contains 3200 L of pure water, with a contaminant solution entering at a rate of 8 L/min, containing 0.11 kg of contaminant per liter. The correct differential equation derived is dC/dt = 0.88 - C(t)/400, where C(t) represents the contaminant amount in kg at time t in minutes. The confusion regarding the variable 't' was clarified, confirming that it does not factor into the rate of contaminant input.

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Homework Statement




A tank contains 3200 L of pure water. A solution that contains 0.11 kg of contaminent per liter enters the tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.

with C representing the amount of contaminent in kg at time t (in minutes), write a differential equation that models this situation.

Homework Equations



possibly int(udv) = uv - int (vdu) (integration by parts)



The Attempt at a Solution



rate in: 8 L /min * .11kg/ L = .88 kg/min I am confused about where to put the variable t here. From my solution, it would appear that .88/t would be right, but then the rate in would decrease over time. This doesn't seem right. Would it be .88t or .88/t or just .88?

rate out: 8 L/min * C(t)/3200L = C(t)/400 kg/min.

DC/dt= rate in - rate out

DC/dt= .88t - C(t)/400

Is this correct? Should I have added the "t" when it is kg/min?



***In my most recent attempt at this problem, I have come up with:
dC/dT = .88 - C(t)/400
 
Last edited:
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dC(t)/dt=.88-C(t)/400 is correct.
 

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