[SOLVED] Application Differential Equation: mixture problem.

An aquarium pool has volume 2 http://www.webassign.net/images/multiply.gif 10^6 liters. The pool initially contains pure fresh water. At t = 0 minutes, water containing 10 grams/liter of salt is poured into the pool at a rate of 60 liters/minute. The salt water instantly mixes with the fresh water, and the excess mixture is drained out of the pool at the same rate (60 liters/minute).

I need to figure out how to "Write a differential equation for S(t), the mass of salt in the pool at time t."


Any help is appreciated.

Quote:

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Originally Posted by Latszer

An aquarium pool has volume 2 http://www.webassign.net/images/multiply.gif 106 liters. The pool initially contains pure fresh water. At t = 0 minutes, water containing 10 grams/liter of salt is poured into the pool at a rate of 60 liters/minute. The salt water instantly mixes with the fresh water, and the excess mixture is drained out of the pool at the same rate (60 liters/minute).

I need to figure out how to "Write a differential equation for S(t), the mass of salt in the pool at time t."


Any help is appreciated.

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Rate of salt in = (10)(60) = 600 gram/min.

Rate of salt out = (C)(60) = (S/212)(60) = 15S/53 gram/min,

where C is the concentration of salt in the tank at time t.

Therefore ....

dS/dt should be in-out so...

600-3S/100000

EDIT: ok nm...that was 10^6 not 106.

Sorry about posting in calculus, I am still in calculus II and forgot I should post this in the DE section (we are doing DE for the last two weeks of class).

I got the equation S(t) to be S = Aexp(3t/100000), if the pool is fresh initially would A jsut be 1?

I got it...

The final answer was S(t)=-20000000exp((-3t)/100000)+20000000

Thanks for the help