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3. A certain chemical reaction problem involving the law of mass action leads to the following equation: 1 (80-x)(60-x) da = k fdt, where k is a constant, and r(t) is the number of kg of reaction product that is present after t minutes, if we start with 80 kg and 60 kg of two reacting substances that follow this law. (a) Integrate on each side, using an appropriate method of integration, to get an equation relating a function of ar to a function of t. (b) Solve your equation from part (a) to get a specific exponential formula for r(t), using the initial condition z(0) = 0. (c) How much reaction product r(t) is present after 15 minutes, assuming that (10) Explain. <= 20?

3. A certain chemical reaction problem involving the law of mass action leads to the following equation: 1 (80-x)(60-x) da = k fdt, where k is a constant, and r(t) is the number of kg of reaction product that is present after t minutes, if we start with 80 kg and 60 kg of two reacting substances that follow this law. (a) Integrate on each side, using an appropriate method of integration, to get an equation relating a function of ar to a function of t. (b) Solve your equation from part (a) to get a specific exponential formula for r(t), using the initial condition z(0) = 0. (c) How much reaction product r(t) is present after 15 minutes, assuming that (10) Explain. <= 20?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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3. A certain chemical reaction problem involving the law of mass action leads to the following equation: 1 √(80-2) (60 - 2) k fdt, dx = k where k is a constant, and z(t) is the number of kg of reaction product that is present after t minutes, if we start with 80 kg and 60 kg of two reacting substances that follow this law. (a) Integrate on each side, using an appropriate method of integration, to get an equation relating a function of a to a function of t. (b) Solve your equation from part (a) to get a specific exponential formula for r(t), using the initial condition z(0) = 0. (c) How much reaction product r(t) is present after 15 minutes, assuming that z(10) = 20? Explain.
Transcribed Image Text:3. A certain chemical reaction problem involving the law of mass action leads to the following equation: 1 √(80-2) (60 - 2) k fdt, dx = k where k is a constant, and z(t) is the number of kg of reaction product that is present after t minutes, if we start with 80 kg and 60 kg of two reacting substances that follow this law. (a) Integrate on each side, using an appropriate method of integration, to get an equation relating a function of a to a function of t. (b) Solve your equation from part (a) to get a specific exponential formula for r(t), using the initial condition z(0) = 0. (c) How much reaction product r(t) is present after 15 minutes, assuming that z(10) = 20? Explain.
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