10. (a) 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). (b) If the rate of excretion of a bio-chemical compound is given by 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?
10. (a) 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).
(b) If the rate of excretion of a bio-chemical compound is given by
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?
plz I want the whole question-answer :)
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