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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