Under some conditions, the result of the movement of a dissolved substance across a cell’s membrane is described by the equation

In this equation, y is the concentration of the substance inside the cell and dy/dt is the rate at which y changes over time. The letters k, A, V, and c stand for constants, k being the permeability coefficient (a property of the membrane), A the surface area of the membrane, V the cell’s volume, and c the concentration of the substance outside the cell. The equation says that the rate at which the concentration changes within the cell is proportional to the difference between it and the outside concentration.

a. Solve the equation for y(t), using y₀ to denote y(0).

b. Find the steady-state concentration, lim_t→∞ y(t).

Transcribed Image Text:

dy dt = A k+(c −y).