. (a) According to Fick’s law , the diffusion of a solute across a cell membrane is given by ′
() =

[ − ()], ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ (1)
where is the area of the cell membrane, is the volume of the cell, () is the
concentration inside the cell at time , is the concentration outside the cell, and is a
constant. If 0 represents the concentration of the solute inside the cell when = 0, then
it can be shown that
() = (0 − )
−

+ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ (2)
(i) Use the last result to find ′().
(ii) Substitute back into Equation (1) to show that (2) is indeed the correct
antiderivative of (1). [8]
(b) If the rate of excretion of a bio-chemical compound is given by

′
() = 0.02
−0.02
,
the total amount excreted by time (in minutes) is ().
(i) Find an expression for ()
(ii) If 0 units are excreted at time = 0, how many units are excreted in 15 minutes?