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- anonymous

Differential equation question

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- anonymous

Differential equation question

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- anonymous

A fish tank initially has 4kg of salt dissolved in 100L of water.

- anonymous

It is decided that this concentration is too high! So, fresh water is mixed at a rate of 10L/mind, while 10L of mixture is removed per minute.

- anonymous

If x kg/L is the concentration of the saltwater solution in the tank t seconds after the fresh water is first added, find the differential equation for x.

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- anonymous

I thought dx/dt = -10x

- anonymous

But i got the answer wrong

- anonymous

water remains constant at 100L. Only salt concentration changing with time

- anonymous

Yep

- anonymous

So concentration = 100x?

- anonymous

i think it will be dx/dt = 4 - 0.4t

- anonymous

sorry 100 dx/dt = 4 - 0.4t

- anonymous

I got the solution, it says 10dx/dt + x = 0

- anonymous

But i dont know how they got that

- anonymous

maybe it's like this : salt concentration is being reduced by 10 X / 100 L where x is salt concentration and water remains constant so only changing thing is 10 L of solution being removed

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