Question: A cell contains a chemical (the solute) dissolved in it at a concentration c(t), and the concentration of the same substance outside the cell is a constant k. By Fick's law, if c(t) and k are unequal, solute moves across the cell wall at a rate proportional to the difference between c(t) and k, toward the region of lower concentration.
(a) Write a differential equation satisfied by c(t).
(b) Solve the differential equation with the initial condition c(0) = c0.
(c) Sketch the solution for c0 = 0.