Math245 SimulProject_Part3_Fall08

Math245 SimulProject_Part3_Fall08 - F a ll20 0 8...

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Fall2008 Friday, Dec. 5 Consider the model for lead transport in the body defined by the block diagram shown on the back side of this page. The mathematical model is given by the following system of ODEs. xt': - (kot+k21 +fu)x1 *ktzxz+kt$s+St(t) x2': k2P1 * (koz+h)xz xjt: kjpl - kr:xs A particular controlled study of lead intake and excretion by healthy volunteers led to the following estimated values for the first-order rate coefficients t4 in the equations. Simulation Problem: Part 3 kor :0.0211; koz : 0.0162; Date Due: hs: 0.000035; k:t : 0.0039. The units of all these rate coefficients are (day) ' . Hence, the independent variable (time) in these equations is assumed to be measured in units of days. The dependent variables x i, i : I , 2,3 , have units of microgyoms (of lead). Task #1. Consider the linear system in the form x : Ax + g(t). a) Find the eigenvalues of the matrix ,4 using values of the rate coefficients given
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Math245 SimulProject_Part3_Fall08 - F a ll20 0 8...

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