27a) drop down box option is (stable, unstable) dC(a) Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then%3DdCdCSolving fordtverifies this differential equation.dtThe rate at which molecules flow out isdC(b) Find the equilibrium of(C-Cm) and use a graphical analysis to determine whether it is stable or unstable. Choose the correct vector field plot below.dtO A.OB.OC.OD.dCdC* dCdtdtdtdtThe equilibrium C=Dis A cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane. We will build a model for this process. Suppose a molecule is present in the cell at aconcentration c(t), and present in its environment at a concentration Com (you may assume Cm is a constant). One model for the diffusion of molecules across the cell membrane is that the rate at which molecules travel through themembrane is proportional to the difference in concentration between the cell and its surroundings. That is, Rate at which molecules flow out of cell = k(C-C.). The constant k is known as the permeability of the membrane; k>0,and k depends on the surface area of the cell and the chemistry of the membrane, as well as the type of molecule. Complete parts (a) through (d).

The rate at which molecules flow out of cell is kC-C∞. The constant k dependent on different factors…

dC (a) Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then %3D dt dC Solving for dC verifies this differential equation. dt The rate at which molecules flow out is- dt dC (b) Find the equilibrium of 7 (C-C) and use a graphical analysis to determine whether it is stable or unstable. Choose the correct vector field plot below. %3D dt O A. OB. OC. OD. dC dC dC dC dt dt dt dt The equilibrium C =D is

dC (a) Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then %3D dt dC Solving for dC verifies this differential equation. dt The rate at which molecules flow out is- dt dC (b) Find the equilibrium of 7 (C-C) and use a graphical analysis to determine whether it is stable or unstable. Choose the correct vector field plot below. %3D dt O A. OB. OC. OD. dC dC dC dC dt dt dt dt The equilibrium C =D is

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

27a) drop down box option is (stable, unstable)

dC
(a) Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then
%3D
dC
dC
Solving for
dt
verifies this differential equation.
dt
The rate at which molecules flow out is
dC
(b) Find the equilibrium of
(C-Cm) and use a graphical analysis to determine whether it is stable or unstable. Choose the correct vector field plot below.
dt
O A.
OB.
OC.
OD.
dC
dC
* dC
dt
dt
dt
dt
The equilibrium C=Dis

A cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane. We will build a model for this process. Suppose a molecule is present in the cell at a
concentration c(t), and present in its environment at a concentration Com (you may assume Cm is a constant). One model for the diffusion of molecules across the cell membrane is that the rate at which molecules travel through the
membrane is proportional to the difference in concentration between the cell and its surroundings. That is, Rate at which molecules flow out of cell = k(C-C.). The constant k is known as the permeability of the membrane; k>0,
and k depends on the surface area of the cell and the chemistry of the membrane, as well as the type of molecule. Complete parts (a) through (d).

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