A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has first order elimination kinetics, so the amount of insulin in the blood will obey the given differential equation, where a> 0 is the rate at which insulin is released into their blood by the pump and k, is the fraction of insulin removed from the blood in one unit of time. dM d =a -k, M (a) Assuming M(0) = 0 (i.e., there is no insulin present in the patient's blood at time t=0), solve the differential equation to find M(t) as a function of t. (b) Find the limit of M(t) as t→0o. (c) Assume that a (the rate of release from the pump) is 1 IU/hr and M(t) → 0.2 IU as t+0o. Calculate k, , the rate of insulin elimination. (a) M(t) =
A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has first order elimination kinetics, so the amount of insulin in the blood will obey the given differential equation, where a> 0 is the rate at which insulin is released into their blood by the pump and k, is the fraction of insulin removed from the blood in one unit of time. dM d =a -k, M (a) Assuming M(0) = 0 (i.e., there is no insulin present in the patient's blood at time t=0), solve the differential equation to find M(t) as a function of t. (b) Find the limit of M(t) as t→0o. (c) Assume that a (the rate of release from the pump) is 1 IU/hr and M(t) → 0.2 IU as t+0o. Calculate k, , the rate of insulin elimination. (a) M(t) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has first order elimination kinetics, so the amount of insulin in the blood will obey the given
differential equation, where a> 0 is the rate at which insulin is released into their blood by the pump and k, is the fraction of insulin removed from the blood in one unit of time.
dM
d =a -k, M
(a) Assuming M(0) = 0 (i.e., there is no insulin present in the patient's blood at time t=0), solve the differential equation to find M(t) as a function of t.
(b) Find the limit of M(t) as t→0o.
(c) Assume that a (the rate of release from the pump) is 1 IU/hr and M(t) → 0.2 IU as t+0o. Calculate k, , the rate of insulin elimination.
(a) M(t) =
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
