Solutes in the bloodstream enter cells through osmosis, which is the diffusion of fluid through a semipermeable membrane. Let C = C (t) be the concentration of a certain solute inside a particular cell. The rate at which the concentration inside the cell is changing is proportional to the difference in the concentration of the solute in the bloodstream and the concentration within the cell. Let k be the constant of proportionality. Suppose the concentration of a solute in the bloodstream is maintained at a constant level of L gm/cubic cm. Find the differential equation that best models this situation. (Use C for the concentration within the cell, not C (t).)

Question

Mathematics

Emmett

8 February, 22:28

Solutes in the bloodstream enter cells through osmosis, which is the diffusion of fluid through a semipermeable membrane. Let C = C (t) be the concentration of a certain solute inside a particular cell. The rate at which the concentration inside the cell is changing is proportional to the difference in the concentration of the solute in the bloodstream and the concentration within the cell. Let k be the constant of proportionality. Suppose the concentration of a solute in the bloodstream is maintained at a constant level of L gm/cubic cm. Find the differential equation that best models this situation. (Use C for the concentration within the cell, not C (t).)

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Conan · Answer 1

since the rate at which concentration inside the cell is proportional to the difference in the concentration of the solute in the blood stream and the concentration within the cell, then the rate of change of concentration within the cell is equals to K (L-C).

Thus, the required differential equation is Δc/Δt = K (L - C).