A cell is put into a fluid containing an 8 milligram/liter concentration of a solute. (This concentration stays constant throughout.) Initially, the concentration of the solute in the cell is 3 milligrams/liter. The solute passes through the cell membrane at such a rate that each minute the increase in concentration in the cell is 40% of the difference between the outside concentration and the inside concentration.
(a) Find the difference equation for yn, the concentration of the solute in the cell after n minutes.
(b) Solve the difference equation from part (a).
(c) Use the solution from part (b) to calculate the concentration of the solute in the cell after 7 minutes?