Non-linear Differential Equation Word Problem
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Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A are used. It is observed that 10 grams of C are formed in 5 minutes.
1. How much is formed in 20 minutes?
2. What is the limiting amount of C after a long time?
3. How much of chemicals A and B remain after a long time?
I originally set up the equation as DR/Dt = k(a-x)(b-x) where k is constant, a=amount of A, b= amount of B, and x = amount of C.
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