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