1. Solve the equation log a. {-8, -9} 72 (x2 - x) = 1. b. {1, 72} c. {8, 9} d. {-8, 9} Q2. The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 200 years? (Round your answer to three decimal places.) a. 14.192 b. 82.263 c. 98.066 d. 0 Q3. For the functions f(x) = x2 + 4 and g(x) = x2 + 1, find the composite function (f g)(x). a. x4 + 5 b. x4 + 17 c. x4 + 2x2 + 5 d. x4 + 8x2 + 17 Q4. Find the amount that results from the investment of $480 invested at 6% compounded quarterly after a period of 3 years. a. $573.90 b. $93.9 c. $565.42 d. $571.69 Q5. Solve the equation (1/3) log a. {9} b. {3, 0} c. {3} d. 2 (x + 6) = log 8 (3x). Q6. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described. a. f -1(x) = (x - 20)/2 b. f -1(x) = x - 20 c. f -1(x) = (x/2) - 20 d. f -1(x) = (x/2) + 20 Q7. Write log 7 (xy)/15 as the sum and/or difference of logarithms. Express powers as factors. a. (1/2) log 7 xy - (1/2) log 7 15 b. (1/2) log 7 x (1/2) log c. (1/2) log 7 x + (1/2) log d. (1/2) log 7 x + (1/2) log y (1/2) log 7 15 7 y - (1/2) log 7 15 7 y - log 7 7 15 Q8. Write log 2 (7m 3n)/k2 as the sum and/or difference of logarithms. Express powers as factors. a. (1/7) log 2 m + (1/3) log 2 n - 2log 2 k b. (1/7) log c. 7log 2 2 m (1/3) log m + 3log d. (7/2) log 2 2 2 n 2log n - 2log m + (3/2) log 2 2 2 k k n - (2/2) log 2 k Q9. Find the inverse of the function and state its domain and range. {(-3, 4), (-1, 5), (0, 2), (2, 6), (5, 7)} a. {(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {2, 4, 5, 6, 7} b. {(-3, -4), (-1, -5), (0, -2), (2, -6), (5, -7)}; D = {-3, -1, 0, 2, 5}; R = {-7, -6, -5, -4, -2} c. {(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)} D = {2, 4, 5, 6, 7}; R = {-3, -1, 0, 2, 5} d. {(3, -4), (1, -5), (0, -2), (-2, -6), (-5, -7)}; D = {3, 1, 0, -2, -5}; R = {-7, -6, -5, -4, -2} Q10. Find the domain of the composite function f g if f(x) = 28/x and g(x) = -8/(x - 7). a. {x | x 7} b. {x | x 0, x 7, x 4} c. {x | x 7, x 0} d. {x | x is any real number} Q11. The graph of a logarithmic function is shown. Select the function which matches the graph. a. y = log 2 (x + 1) b. y = log 2 (x - 1) c. y = log 2 x d. y = log 2 x-1 Q12. If 5x = 6,what does 5-2x equal? a. 1/36 b. 36 c. 1/12 d. -36 Q13. Find the exact value of the logarithmic expression ln e. a. 0 b. -1 c. 1 d. e Q14. The graph of a one-to-one function f(x) = x + 2 is given. Draw the graph of the inverse function f-1 as a dashed line or curve. a. b. Q15. The graph of an exponential function is given. Match the graph to one of the following functions. a. f(x) = 3x b. f(x) = -3x c. f(x) = 3-x d. f(x) = -3-x Q16. If f(x) = 4x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer. a. (log 4 12, 12) b. (log 4 12, 4) c. (log 4 12, 0) d. (12, 12) Q17. Change the exponential expression 5-3 = 1/125 to an equivalent expression involving a logarithm. a. log -3 1/125 = 5 b. log 5 1/125 = -3 c. log 5 -3 = 1/125 d. log 1/125 5 = -3 Q18. In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation P(t) = 240/(5 + 54.99e-0.0208t), where t is the number of years since 1990. Estimate the year when the population will be 21 million. a. approximately the year 2093 b. approximately the year 2041 c. approximately the year 2088 d. approximately the year 2016 Q19. Solve the equation log a. {-7} 4 (x + 2) = -1 b. {-7/4} c. {9/4} d. {9} Q20. Solve the equation 3(1 + 2x) = 243. a. {81} b. {2} c. {-2} d. {6} Q21. Solve using elimination. a. x = 5, y = 9; x = -5, y = 9; x = 5, y = -9; x = -5, y = -9 or (5, 9), (-5, 9), (5, -9), (-5, -9) b. x = 5, y = 9; x = 9, y = 5; x = -5, y = -9; x = -9, y = -5 or (5, 9), (9, -5), (-5, -9), (-9, -5) c. x = -5, y = -9; x = -9, y = -5 or (-5, -9), (-9, -5) d. x = 5, y = -9; x = 5, y = 9 or (5, -9), (5, 9) Q22. Write a system of linear inequalities that has the given graph. a. b. c. d. Q23. Graph the inequality x + y < -5. a. b. c. d. Q24. Solve the system of equations. a. x = -4, y = 4, z = -3; (-4, 4, -3) b. x = -3, y = 4, z = -4; (-3, 4, -4) c. x = -4, y = -3, z = 4; (-4, -3, 4) d. inconsistent Q25. Write the partial fraction decomposition of the rational expression x/(x 2 - 9x + 20). a. -4/(x - 4) + 5/(x - 5) b. -5/(x - 4) + 4/(x - 5) c. 4/(x - 4) + -5/(x - 5) d. -4/(x - 4) + -5/(x - 5) Q26. Write the system of equations associated with the augmented matrix. Do not solve. a. b. c. Q27. Solve the system of equations using Cramer's Rule if it is applicable. a. x = 9, y = 2, z = 5; (9, 2, 5) b. x = 8, y = 4, z = 5; (8, 4, 5) c. x = 4, y = 5, z = 4; (4, 5, 4) d. x = 8, y = -4, z = -5; (8, -4, -5) Q28. Perform the row operations on the given augmented matrix. a. b. c. d. Q29. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. a. x = -2, y = -1, z = 0; (-2, -1, 0) b. x = -2, y = 0, z = -1; (-2, 0, -1) c. x = 0, y = -2, z = -1; (0, -2, -1) d. x = 0, y = -1, z = -2; (0, -1, -2) Q30. Write the augmented matrix for the system. a. b. c. d. Q31. a. b. c. d. Q32. Solve the system of equations by substitution. a. x = 2, y = 9; (2, 9) b. x = 3, y = 9; (3, 9) c. x = 3, y = 8; (3, 8) d. x = 2, y = 8; (2, 8) Q33. Solve the system of equations using substitution. a. x = 2, y = 4; x = 2, y = -4; x = -2, y = 0 or (2, 4), (2, -4), (-2, 0) b. x = 2, y = 4; x = -2, y = 0 or (2, 4), (-2, 0) c. x = 2, y = 4; x = 2, y = -4 or (2, 4), (2, -4) d. x = 2, y = 4 or (2, 4) Q34. a. b. c. d. Q35. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. a. x = 2, y = 3, z = -7; (2, 3, -7) b. x = 1, y = 3, z = -4; (1, 3, -4) c. x = 5, y = 13/2, z = -3; (5, 13/2, -3) d. x = 1, y = -3, z = -16; (1, -3, -16) Q36. Find the value of the determinant. a. 45 b. 27 c. 15 d. -27 Q37. Use properties of determinants to find the value of the second determinant, if the value of the first is known. a. 9 b. -18 c. 18 d. -9 Q38. Write the partial fraction decomposition of the rational expression (4x 3 + 4x2)/(x2 + 5)2. a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2 b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2 c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2 d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2 Q39. Find the inverse of the matrix. Be sure to check your answer. a. b. c. d. Q40. Solve the system of equations. If the system has no solution, say that it is inconsistent. a. y = -2x + 7, where x is any real number or {(x, y) | y = -2x + 7, where x is any real number} b. y = 2x + 7, where x is any real number or {(x, y) | y = 2x + 7, where x is any real number} c. x = -2y + 7, where y is any real number or {(x, y) |x = -2y + 7, where y is any real number} d. inconsistent