Active oxygen and free radicals are believed to be exacerbating factors in causing cell injury and aging in living tissue . Researchers are therefore interested in understanding the protective role of natural antioxidants. In the study of one such antioxidant (Hsian-tsao leaf gum), the antioxidation activity of the substance has been found to depend on concentration in the following way: dA(c)\dc=k[L−A(c)], A(0)=0.dA(c)dc=k[L−A(c)], A(0)=0. In this equation, the dependent variable AA is a quantitative measure of antioxidant activity at concentration cc. The constant LL represents a limiting or equilibrium value of this activity, and kk a positive rate constant. Let B(c)=A(c)−L and reformulate the given initial value problem in terms of this new dependent variable, B.dB(c)/dc= B(0)= Solve the new initial value problem for B(c)and then determine the quantity A(c).A(c)= Does the activity A(c) ever exceed the value L? ? yes no Determine the concentration at which 95% of the limiting antioxidation activity is achieved. (Your answer is a function of the rate constant kk.)c=
Active oxygen and free radicals are believed to be exacerbating factors in causing cell injury and aging in living tissue . Researchers are therefore interested in understanding the protective role of natural antioxidants. In the study of one such antioxidant (Hsian-tsao leaf gum), the antioxidation activity of the substance has been found to depend on concentration in the following way: dA(c)\dc=k[L−A(c)], A(0)=0.dA(c)dc=k[L−A(c)], A(0)=0. In this equation, the dependent variable AA is a quantitative measure of antioxidant activity at concentration cc. The constant LL represents a limiting or equilibrium value of this activity, and kk a positive rate constant. Let B(c)=A(c)−L and reformulate the given initial value problem in terms of this new dependent variable, B.dB(c)/dc= B(0)= Solve the new initial value problem for B(c)and then determine the quantity A(c).A(c)= Does the activity A(c) ever exceed the value L? ? yes no Determine the concentration at which 95% of the limiting antioxidation activity is achieved. (Your answer is a function of the rate constant kk.)c=
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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Active oxygen and free radicals are believed to be exacerbating factors in causing cell injury and aging in living tissue . Researchers are therefore interested in understanding the protective role of natural antioxidants. In the study of one such antioxidant (Hsian-tsao leaf gum), the antioxidation activity of the substance has been found to depend on concentration in the following way:
dA(c)\dc=k[L−A(c)], A(0)=0.dA(c)dc=k[L−A(c)], A(0)=0.
In this equation, the dependent variable AA is a quantitative measure of antioxidant activity at concentration cc. The constant LL represents a limiting or equilibrium value of this activity, and kk a positive rate constant.
- Let B(c)=A(c)−L and reformulate the given initial value problem in terms of this new dependent variable, B.
dB(c)/dc=
B(0)= - Solve the new initial value problem for B(c)and then determine the quantity A(c).
A(c)=
Does the activity A(c) ever exceed the value L? ? yes no - Determine the concentration at which 95% of the limiting antioxidation activity is achieved. (Your answer is a function of the rate constant kk.)
c=
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