EGM_3344_Exams3&4_2009

EGM_3344_Exams3&4_2009 - Sorting Number: _...

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Sorting Number: ______________________ Fall 2009 1 INTRODUCTION TO NUMERICAL METHODS OF ENGINEERING ANALYSIS EGM 3344 EXAM 2 HANDWRITTEN (50 points) AND PROGRAMMING (50 points) General instructions: This exam is closed book and closed notes except for one page, front and back. Nothing electronic is allowed except for a calculator. The only allowable calculator functions are +, -, *, /, sin, cos, and ^, and sqrt. All work on this exam should be done individually, and you are reminded that the University of Florida has an honor code. The instructor has a zero-tolerance policy for cheating on exams. Any suspected violation of the honor code will be reported to Student Judicial Affairs. If you are found guilty, you may receive a permanent mark on your UF academic transcript and will receive an automatic failing grade in this course. Please show all your work clearly and neatly, as partial credit will be given if it is clear that you understood the concepts required to solve the problem. All six problems should be completed. No credit will be given without a signature and date on the honor code statement at the bottom of the last page of this exam .
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Sorting Number: ______________________ Fall 2009 2 Problem 1 (Handwritten) – Nonlinear Regression. (13 points) A University of Florida researcher performs an experiment to determine the growth rate of bacteria k (bacteria per day) as a function of oxygen consumption c (mg/L). Tabulated data from the experiment and a corresponding plot of the data (open circles) are provided below, along with a regression fit of the data performed by the researcher (solid line). c 0.5 0.8 1.5 2.5 4 k 1.1 2.3 5.2 7.7 8.9 0 1 2 3 4 5 0 2 4 6 8 10 c (mg/L) k (bacteria per day) To generate this regression fit, the researcher modeled the data using the nonlinear relationship 2 1 2 2 ac k = + (1) and linearized this equation using transformation of variables. After performing the regression fit for the linearized model, the researcher calculated the values of the regression coefficients 1 a and 2 a for the original nonlinear model and used these values in Eq. (1) to generate the solid line shown in the figure above. a) Use transformation of variables to derive the linearized version of Eq. (1) that was used by the researcher for regression analysis. Assume the linearized model is given by yp xq = + where p and q are regression coefficients. Provide expressions in the spaces below for y as a function of k , x as a function of c , and how p and q as functions of 1 a and 2 a . y = _____________________________ x = _____________________________ p = _____________________________ q = _____________________________ Problem continued on next page . . .
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Sorting Number: ______________________ Fall 2009 3 b) Formulate a linear system of equations Ax b = that could be solved for the regression coefficients p and q in the linearized model (Note: DO NOT solve these equations). Keep only two significant figures for all values used in your linear system of equations. Record you’re A matrix and b
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EGM_3344_Exams3&4_2009 - Sorting Number: _...

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