Suppose that no chemical re-enters the cell. This should look like the differential equation for a population. What would be happening to the concentration?
The derivation of the movement of chemical assumed that chemical moved as easily into the cell as out of it. If the membrane can act as a filter, the rates at which chemical enters and leaves might differ, or might depend on the concentration itself. In each of the following cases, draw a diagram illustrating the situation and write the associated differential equation. Let C be the concentration inside the cell, r the concentration outside, and β the constant of proportionality relating the concentration and the rate.