EGN 3433

NAME

The concentration of a drug in a person's stomach can be described with the following linear

ODE.

Where

●

dc

dt

= - KA, (c-cs)

c is the concentration of the drug in the stomach

k is the mass transfer transfer coefficient

(4.1)

A, is the ratio of the surface area of the stomach lining to its volume

Sep 14, 2023

B. What is the forcing function?

c, is the concentration of the drug in the blood stream, which can be a function of time.

A. What are the independent and the dependent variables?

dy

C. Rewrite the ODE in the form: t + y = f(t) where y and x are the dependent and

dx

independent variables, respectively, Given that, k = : 0.9 m/s, A, = .01 m¯¹, what is the value

T? Use correct units!

1 EGN 3433

Sep 14, 2023

D. If at time zero, c = 12 mg/ml, what is the amount of time needed for the concentration of

the drug in the stomach to be 3 mg/mL? Use separation of variables. Here you can assume,

that Cs = .01 mg/mL. In the problem, k 0.9 m/s, A. = .01 m¯¹.

=

E. Let's say that c¸ is not a constant, but slowly increases with time. For instance,

mg

cs(t) = 0.001- t +0.002.

ml. s

mg

ml

Can you use separation of variables to solve? Why or why not? Suggest an alternative

technique that you can use to solve.

2