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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
Transcribed Image Text: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).
Transcribed Image Text: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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