According to Fick’s law , the diffusion of a solute across a cell membrane is given by c
′
(t) =
kA
V
[C − c(t)], ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ (1)

where A is the area of the cell membrane, V is the volume of the cell, c(t) is the
concentration inside the cell at time t, C is the concentration outside the cell, and k is a
constant. If c0 represents the concentration of the solute inside the cell when t = 0, then
it can be shown that

c(t) = (c0 − C)e
−
KAt
V + M ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ (2)

(i) Use the last result to find c′(t).
(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 [4]

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