10. (a) According to Fick's law , the diffusion of a solute across a cell membrane is given by kA c'(t) =D ㅠ[C-c(t)].… · (1) V 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 co represents the concentration of the solute inside the cell when t = 0, then it can be shown that _KAt c(t) = (co – C)eT +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 kA c'(t) =D ㅠ[C-c(t)].… · (1) V 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 co represents the concentration of the solute inside the cell when t = 0, then it can be shown that _KAt c(t) = (co – C)eT +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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you answer this question all of it including section a and b please
![10. (a) According to Fick's law, the diffusion of a solute across a cell membrane is given by
c'(t) =
kA
[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 co represents the concentration of the solute inside the cell when t = 0, then
it can be shown that
KAt
c(t) = (co - C)e
+ 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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bc1bdb6-7209-42f8-8e8b-501c54e2d6e6%2F8b2f6c05-c06f-40ef-925c-4b782753e3fe%2F821liq9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10. (a) According to Fick's law, the diffusion of a solute across a cell membrane is given by
c'(t) =
kA
[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 co represents the concentration of the solute inside the cell when t = 0, then
it can be shown that
KAt
c(t) = (co - C)e
+ 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?
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