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crosssbow

create a 3 by3 system of ODE IVP from this problem: Suppose three chemical species are in a process of reaction, where every minute 20% of chemical A becomes chemical B, and 25% of chemical B become chemical C. There is no supply of chemical A. The reaction stops at chemical C. At present, there are 100 grams of chemical A, 20 grams of chemical B, and no chemical C. We are interested in the First 10 minutes of the reaction.

  • one year ago
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  1. UnkleRhaukus
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    so we need to find three equations

    • one year ago
  2. crosssbow
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    yes, i said x , y, and z

    • one year ago
  3. crosssbow
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    x=chem A y=chem B z=chem C

    • one year ago
  4. crosssbow
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    dx/dt=?? dy/dt=??? dz/dt=??

    • one year ago
  5. crosssbow
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    and i believe i know the interval [0,10]

    • one year ago
  6. crosssbow
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    since we are intrested in the first 10 min

    • one year ago
  7. UnkleRhaukus
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    so \[\frac{\text dA}{\text dt}=80\%A\]

    • one year ago
  8. crosssbow
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    why?

    • one year ago
  9. UnkleRhaukus
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    every minute 20% of chemical A becomes chemical B so every minute chemical A becomes 80% of was before

    • one year ago
  10. crosssbow
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    okay, that makes sense, how about for dB/dt?

    • one year ago
  11. UnkleRhaukus
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    every minute 20% of chemical A becomes chemical B, and 25% of chemical B become chemical C

    • one year ago
  12. crosssbow
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    20%A-25%B

    • one year ago
  13. UnkleRhaukus
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    and the last one/

    • one year ago
  14. crosssbow
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    i am not sure , maybe just 25%B??

    • one year ago
  15. crosssbow
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    ?

    • one year ago
  16. UnkleRhaukus
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    i think thats right

    • one year ago
  17. crosssbow
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    okay thanks

    • one year ago
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