Question

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.

Answer 1

so we need to find three equations

Answer 2

yes, i said x , y, and z

Answer 3

x=chem A

y=chem B

z=chem C

Answer 4

dx/dt=??

dy/dt=???

dz/dt=??

Answer 5

and i believe i know the interval [0,10]

Answer 6

since we are intrested in the first 10 min

Answer 7

so
\[\frac{\text dA}{\text dt}=80\%A\]

Answer 8

why?

Answer 9

every minute 20% of chemical A becomes chemical B

so every minute chemical A becomes 80% of was before

Answer 10

okay, that makes sense, how about for dB/dt?

Answer 11

every minute 20% of chemical A becomes chemical B, and 25% of chemical B become chemical C

Answer 12

20%A-25%B

Answer 13

and the last one/

Answer 14

i am not sure , maybe just 25%B??

Answer 15

?

Answer 16

i think thats right

Answer 17

okay thanks