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cvxvxcv - A Dec 3,2004 MATH I I 3 TEST 3 NAME(4.3-6.3...

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Unformatted text preview: A Dec. 3,2004 MATH I I 3 - TEST 3 NAME: (4.3-6.3) SECTION: Instructions: Do all problems in the spaces provided. Mark your answers clearly and write them in simplified form. You must show all appropriate work in order to receive credit for an answer. You may use graphing calculators, but show work algebraically and find exact answers where indicated. 1. The amount of money, A, in an account after t years, invested at a rate, r, is given by : A = 5400e-05t (a) What was the amount of the original investment ? [6] (b) Determine the length of time it will take the original investment to triple. [8] 2. An inheritance of $50,000 was divided among three investments yielding a total of $3940 in interest per year. The interest rates for the three investments were 5%, 7% and 10% . SET UP the system of 3 equations you would need to find the amount of money placed in each investment if the 10% investment was twice as much as the 7% investment. Specify clearly what each variable represents. Set up the system only, you do not need to solve it. [8] A page 1 of 4 3. (a) Evaluate the following, correct to 3 decimal places, by first writing the expression in terms of natural logarithms: log 4 245 [5] (b) Write the following as a single logarithmic expression: [6] élnbc2 —25)+%lnx6 —3ln(x—l) 4. (a) Does the function y = .4066 '01“ represent exponential growth or decay? [4] (b) The radioactive element radium has a half-life of 1620 years. An amount of radium decays according to the model A = Aoekt . If the initial amount present is 10 grams, determine the amount that is left after 1620 years. [5] 5. Solve for x. Give your result as an exact answer in simplest form. log4 x+log4(x-6) = 2 [8] A page 2 of 4 .____———__._________._____________—___..._____ ._.__._ . , 6. Solve for x. Show all work, and write your answer first as an exact answer, then as a decimal correct to 2 decimal places. e2“7 — 4 = 300 [6] 7. (a) Solve the following system of equations, showing your work algebraically. Write your answer as (an)ordered pair(s). [8] (b) A few steps in row-reducing the following matrix have been performed. Fill in the missing numbers: [8] l 2 —l 0 l 2 — l; 2 —21—2§9—>0 5 4 —11E14 0-9 8. (a) Write the augmented matrix that is associated with the following system of equations [5] x+2y+z= 4 2x-y+z=8 y-z=~4 (b) Solve the above system of equations by a method of your choice. Show your work. [7] A page 3 of 4 —___—___—_____________.~_.—_____________—._”.—_._.. x+y<4 3x—3y26 9. (a) Sketch the following system of inequalities. > O x ._ yZO W (b) Write the coordinates of all the corner points of the solution region of the above system of inequalities. W Copy the following pledge and sign your name: I pledge on my honor that I have not given or received any unauthorized assistance on this examination. A page 4 of 4 ...
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