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baddinlol

  • 2 years ago

Differential equation question

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  1. baddinlol
    • 2 years ago
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    A fish tank initially has 4kg of salt dissolved in 100L of water.

  2. baddinlol
    • 2 years ago
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    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.

  3. baddinlol
    • 2 years ago
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    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.

  4. baddinlol
    • 2 years ago
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    I thought dx/dt = -10x

  5. baddinlol
    • 2 years ago
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    But i got the answer wrong

  6. suvesh253
    • 2 years ago
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    water remains constant at 100L. Only salt concentration changing with time

  7. baddinlol
    • 2 years ago
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    Yep

  8. baddinlol
    • 2 years ago
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    So concentration = 100x?

  9. suvesh253
    • 2 years ago
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    i think it will be dx/dt = 4 - 0.4t

  10. suvesh253
    • 2 years ago
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    sorry 100 dx/dt = 4 - 0.4t

  11. baddinlol
    • 2 years ago
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    I got the solution, it says 10dx/dt + x = 0

  12. baddinlol
    • 2 years ago
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    But i dont know how they got that

  13. suvesh253
    • 2 years ago
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    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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