4. Matrix models can be used to describe the flow of certain toxins , like lead, betweencompartments of a biological system. For example, lead enters the human body by inhaling oringesting lead particles. These particles are diffused into the tissue such as kidney and liver andinto the bloodstream.Let Xn represent the amount of lead in the blood ( in micrograms ) and let Yn represent theamount in the tissue at the start of a certain month.A model for calculating the levels a month later is given by (*1) = ( 02) )(Xn+1Yn+1.Answer these questions , use the next blank page for your work. Only write the answers here.a. Find the fraction of lead in the system that will be in the blood and in the tissues in the long run .b. Find a formula that gives the amount Xn and Yn for any month. Since you do not have an initialcondition, you will find equations that measure the amounts for any starting value.Xn =Yn =

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4. Matrix models can be used to describe the flow of certain toxins , like lead, between compartments of a biological system. For example, lead enters the human body by inhaling or ingesting lead particles. These particles are diffused into the tissue such as kidney and liver and into the bloodstream. Let Xn represent the amount of lead in the blood ( in micrograms ) and let Yn represent the amount in the tissue at the start of a certain month. .04) (X, .04 .02. 39 A model for calculating the levels a month later is given by (*1) = ( 05) \Yn+1. Answer these questions , use the next blank page for your work. Only write the answers here. a. Find the fraction of lead in the system that will be in the blood and in the tissues in the long run . b. Find a formula that gives the amount Xn and Yn for any month. Since you do not have an initial condition, you will find equations that measure the amounts for any starting value. Xn = Yn =

4. Matrix models can be used to describe the flow of certain toxins , like lead, between compartments of a biological system. For example, lead enters the human body by inhaling or ingesting lead particles. These particles are diffused into the tissue such as kidney and liver and into the bloodstream. Let Xn represent the amount of lead in the blood ( in micrograms ) and let Yn represent the amount in the tissue at the start of a certain month. .04) (X, .04 .02. 39 A model for calculating the levels a month later is given by (*1) = ( 05) \Yn+1. Answer these questions , use the next blank page for your work. Only write the answers here. a. Find the fraction of lead in the system that will be in the blood and in the tissues in the long run . b. Find a formula that gives the amount Xn and Yn for any month. Since you do not have an initial condition, you will find equations that measure the amounts for any starting value. Xn = Yn =

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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Question

4. Matrix models can be used to describe the flow of certain toxins , like lead, between
compartments of a biological system. For example, lead enters the human body by inhaling or
ingesting lead particles. These particles are diffused into the tissue such as kidney and liver and
into the bloodstream.
Let Xn represent the amount of lead in the blood ( in micrograms ) and let Yn represent the
amount in the tissue at the start of a certain month.
A model for calculating the levels a month later is given by (*1) = ( 02) )
(Xn+1
Yn+1.
Answer these questions , use the next blank page for your work. Only write the answers here.
a. Find the fraction of lead in the system that will be in the blood and in the tissues in the long run .
b. Find a formula that gives the amount Xn and Yn for any month. Since you do not have an initial
condition, you will find equations that measure the amounts for any starting value.
Xn =
Yn =

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