posted by Catherine
I'm having trouble getting started. Steve said it's similar to another question I asked but I don't know how to begin. Any help?
Suppose a cell of volume V cc is surrounded by a homogeneous chemical solution of concentration C g/cc. Let y denote the concentration of the solute inside the cell at any time t and suppose that, initially, the concentration is y0. Fick's law, named after the German physiologist Adolf Fick (1829-1901), states that the rate of change of the concentration of solute inside the cell at any time t is proportional to the difference between the concentration of the solute outside the cell and the concentration inside the cell and inversely proportional to the volume of the cell. Fick's law may be expressed as the differential equation.
dy/dt = k/V(C-Y)
y(0) = y_0
Use separation of variables to solve the differential equation given above, where k, V, C, and y0 are constants with
C − y > 0.
(Note: The constant of proportionality k depends on the area and permeability of the cell membrane.)
y = ?????
check your previous posts. This one is explained there.