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.
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UnkleRhaukus
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so we need to find three equations
crosssbow
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yes, i said x , y, and z
crosssbow
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x=chem A
y=chem B
z=chem C
crosssbow
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dx/dt=??
dy/dt=???
dz/dt=??
crosssbow
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and i believe i know the interval [0,10]
crosssbow
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since we are intrested in the first 10 min
UnkleRhaukus
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so
\[\frac{\text dA}{\text dt}=80\%A\]
crosssbow
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why?
UnkleRhaukus
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every minute 20% of chemical A becomes chemical B
so every minute chemical A becomes 80% of was before
crosssbow
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okay, that makes sense, how about for dB/dt?
UnkleRhaukus
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every minute 20% of chemical A becomes chemical B, and 25% of chemical B become chemical C
crosssbow
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20%A-25%B
UnkleRhaukus
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and the last one/
crosssbow
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i am not sure , maybe just 25%B??
crosssbow
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?
UnkleRhaukus
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i think thats right
crosssbow
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okay thanks