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 theequilibrium 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 for1the perturbation to drop to a factorC1of its initial value (i.e., for C(t) to drop from Co + C, to Co +-). If the single compartment obeys the single-compartmentdCdifferential equationdt7 (G - C), complete parts (a) and (b).V.....O B. C(t) = Co - (Co-Ci) •O C. C(1) = C, - (G +c,) evtO D. C(t) = Co - (Co +Ci) eSubstitute C, for C, and Co + C, for C(0) into the single-compartment equation.C(t) = Co + CeVNow 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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Description: 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 theequilibrium concentration is Co. Then, to measure TR, perturb the concentration s

At t = 0 units, C(t) = C(0) = Co + C1 At t = TR units, C(t) = C(TR) = Co + C1/e dCdt= qVC1-C

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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 =

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

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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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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