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The stability of the equilibrium concentration in a single compartment is often quantified using TR, which is called the time to return to equilibrium. Suppose that the equilibrium concentration is Co. Then, to measure TR, perturb the concentration slightly from Co to Co +C,. Then TR is defined to be the time that the tank takes for the perturbation to drop to a factor e C1 -). If the single compartment obeys the single-compartment of its initial value (i.e., for C(t) to drop from Co + C, to Co + - dC differential equation complete parts (a) and (b). %3D dt ..... O B. C(t) = Co - (Co -Ci) O C. C(t) = C, - O D. C(1) = Co - (Co + Ci) e Substitute Co for C, and Co + C, for C(0) into the single-compartment equation. C(t) = Co + C,e V Now find TR such that C(TR) =U. Setting this expression for C(TR) equal to the expression for C(t) and solving for t gives TR =

The stability of the equilibrium concentration in a single compartment is often quantified using TR, which is called the time to return to equilibrium. Suppose that the equilibrium concentration is Co. Then, to measure TR, perturb the concentration slightly from Co to Co +C,. Then TR is defined to be the time that the tank takes for the perturbation to drop to a factor e C1 -). If the single compartment obeys the single-compartment of its initial value (i.e., for C(t) to drop from Co + C, to Co + - dC differential equation complete parts (a) and (b). %3D dt ..... O B. C(t) = Co - (Co -Ci) O C. C(t) = C, - O D. C(1) = Co - (Co + Ci) e Substitute Co for C, and Co + C, for C(0) into the single-compartment equation. C(t) = Co + C,e V Now find TR such that C(TR) =U. Setting this expression for C(TR) equal to the expression for C(t) and solving for t gives TR =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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The stability of the equilibrium concentration in a single compartment is often quantified using TR: which is called the time to return to equilibrium. Suppose that the equilibrium concentration is Co. Then, to measure TR, perturb the concentration slightly from C, to Co + C,. Then TR is defined to be the time that the tank takes for 1 the perturbation to drop to a factor C1 of its initial value (i.e., for C(t) to drop from Co + C, to Co +-). If the single compartment obeys the single-compartment dC differential equation dt 7 (G - C), complete parts (a) and (b). V ..... O B. C(t) = Co - (Co-Ci) • O C. C(1) = C, - (G +c,) evt O D. C(t) = Co - (Co +Ci) e Substitute C, for C, and Co + C, for C(0) into the single-compartment equation. C(t) = Co + Ce V Now find TR such that C (TR) =U setting this expression for C (TR) equal to the expression for C(t) and solving for t gives TR =
Transcribed Image Text:The stability of the equilibrium concentration in a single compartment is often quantified using TR: which is called the time to return to equilibrium. Suppose that the equilibrium concentration is Co. Then, to measure TR, perturb the concentration slightly from C, to Co + C,. Then TR is defined to be the time that the tank takes for 1 the perturbation to drop to a factor C1 of its initial value (i.e., for C(t) to drop from Co + C, to Co +-). If the single compartment obeys the single-compartment dC differential equation dt 7 (G - C), complete parts (a) and (b). V ..... O B. C(t) = Co - (Co-Ci) • O C. C(1) = C, - (G +c,) evt O D. C(t) = Co - (Co +Ci) e Substitute C, for C, and Co + C, for C(0) into the single-compartment equation. C(t) = Co + Ce V Now find TR such that C (TR) =U setting this expression for C (TR) equal to the expression for C(t) and solving for t gives TR =
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