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.

Solution Summary

A Nnon-linear differential equation word problem is solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

...Nonlinear Differential Equations and Chemical Reactions are investigated ... in the statement of the problem: The words ... ... From equation (10) we ﬁnd 1 k= . (11 ...

... so we have to solve for an equations system for ... number of noisy data points, the difference between vertical ... For nonlinear least squares fitting to a number of ...

... (d) What is the difference between a regression residual and the true random ... Regression may be linear or nonlinear. ... (a) Write the fitted regression equation. ...

... Create an equation of a nonlinear function and provide ... to the following: What is the difference between domain ... there an instance when a linear equation is not ...

... to fit the regression, with fitted equation and R2. ... 2. There may exist better nonlinear relationship between the ... The only difference is that we need to select ...

... is a biased estimator (because of the non-linear relationship between the ... It is calculated by the formula SEM = s / √n ... (a) Explain the difference between the ...

Please help solve the following nonlinear system: ... The first is in MS Word format, while the other is in Adobe pdf format. ... Our differential equation is: ...

... This equation means that you subtract to find the ... Take that difference and divide by the actual value ... however, this trend variation is non-linear and the ...

... programming b) probabilistic c) non-linear programming d ... 6. Profit is the difference between total ... relationship between variables, parameters, and equations. ...