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baddinlol Group Title

Differential equation question

  • 2 years ago
  • 2 years ago

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  1. baddinlol Group Title
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    A fish tank initially has 4kg of salt dissolved in 100L of water.

    • 2 years ago
  2. baddinlol Group Title
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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.

    • 2 years ago
  3. baddinlol Group Title
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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.

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

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

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

    • 2 years ago
  7. baddinlol Group Title
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    Yep

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

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

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

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

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

    • 2 years ago
  13. suvesh253 Group Title
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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

    • 2 years ago
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