Two substances A and B are combined to form a product C. The formation of the product is proportional to the time the reactants are combined. The final product is composed of three parts of A for every part of B. If initially A is 50 lbs and B is 60 lbs, and 10 lbs of the product are formed after 45 mins., find the time it takes for the reaction to form 25 lbs. Use the mathematical model provided for variable names.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Two substances A and B are combined to form a product C. The formation of the product is proportional to the time the reactants are combined. The final product is composed of three parts of for every part of B. If initially A is 50 lbs and B is 60 lbs, and 10  lbs of the product are formed after 45 mins., find the time it takes for the reaction to form 25 lbs.

 

Use the mathematical model provided for variable names.

 

Chemical Reactions
Mathematical Model
dx
-k (m, – r,x)(m, – x)
dt
where
•x = amount of final product in mass units
•t = time
• m1 = amount of reactant 1 in mass units
•m2 = amount of reactant 2 in mass units
r1 = ratio of composition of reactant 1 to final
product
l2 = ratio of composition of reactant 2 to final
product
Transcribed Image Text:Chemical Reactions Mathematical Model dx -k (m, – r,x)(m, – x) dt where •x = amount of final product in mass units •t = time • m1 = amount of reactant 1 in mass units •m2 = amount of reactant 2 in mass units r1 = ratio of composition of reactant 1 to final product l2 = ratio of composition of reactant 2 to final product
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