1. The value of a particular investment follows a pattern of exponential growth. You invested money in a money market account. The value of your investment t years after your initial investment is given by the exponential growth model A = 5100e 0.047t. How much did you initially invest in the account? a. $2550.00 b. $5345.42 c. $5100.00 d. $239.70 Q2. 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 Q3. Find functions f and g so that f g = H(x) = (5 - 2x3)2. a. f(x) = 5 - 2x3 ; g(x) = x2 b. f(x) = (5 - 2x)3 ; g(x) = x2 c. f(x) = x2 ; g(x) = 5 - 2x3 d. f(x) = x3 ; g(x) = (5 - 2x)2 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. 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. Q6. Solve the equation log a. {-8, -9} 72 (x2 - x) = 1. b. {1, 72} c. {8, 9} d. {-8, 9} Q7. Find the amount that results from the investment of $12,000 invested at 5% compounded quarterly after a period of 8 years. a. $5857.57 b. $17,729.47 c. $17,857.57 d. $17,637.10 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 2 2 n 2log n - 2log 2 k 2 k d. (7/2) log 2 m + (3/2) log Q9. Solve the equation log a. {-7} 4 2 n - (2/2) log 2 k (x + 2) = -1 b. {-7/4} c. {9/4} d. {9} Q10. The function f(x) = 6x - 1 is one-to-one. Find its inverse. a. f -1(x) = (x/6) - 1 b. f -1(x) = (x - 1)/6 c. f -1(x) = (x + 1)/6 d. f -1(x) = (x/6) + 1 Q11. If 5x = 6,what does 5-2x equal? a. 1/36 b. 36 c. 1/12 d. -36 Q12. 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} Q13. 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 Q14. Find the exact value of the logarithmic expression ln e. a. 0 b. -1 c. 1 d. e Q15. Solve the equation 8x - 4 = 324x. a. {-12/17} b. {-4/3} c. {-2} d. {-4/17} Q16. 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 Q17. Solve the equation (1/3) log a. {9} 2 (x + 6) = log 8 (3x). b. {3, 0} c. {3} d. Q18. Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write ln 10 in terms of a and b. a. ab b. a - b c. a + b d. ln a + ln b Q19. A thermometer reading 8C is brought into a room with a constant temperature of 20C. If the thermometer reads 18C after 5 minutes, what will it read after being in the room for 7 minutes? Assume the cooling follows Newton's Law of Cooling: U = T + (U o T)ekt. (Round your answer to two decimal places.) a. 1.6C b. 20.98C c. 19.02C d. 20C Q20. 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 Q21. 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 Q22. Solve the system of equations using substitution. a. x = -6, y = 7; x = -7, y = 6 or (-6, 7), (-7, 6) b. x = -6, y = -7; x = -7, y = -6 or (-6, -7), (-7, -6) c. x = 6, y = -7; x = 7, y = -6 or (6, -7), (7, -6) d. x = 6, y = 7; x = 7, y = 6 or (6, 7), (7, 6) Q23. 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) Q24. A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 7 inches longer than the width. Find the width. a. 18 in. b. 29 in. c. 11 in. d. 25 in. Q25. 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) Q26. 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) Q27. Write the system of equations associated with the augmented matrix. Do not solve. a. b. c. Q28. 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 Q29. 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) Q30. Solve the system of equations using Cramer's Rule if it is applicable. a. x = -4, y = 3; (-4, 3) b. x = -3, y = -4; (-3, -4) c. x = 4, y = 3; (4, 3) d. x = 3, y = 4; (3, 4) Q31. Find the inverse of the matrix. Be sure to check your answer. a. b. c. d. Q32. Perform the row operations on the given augmented matrix. a. b. c. d. Q33. Graph the solution set of the system of inequalities or indicate that the system has no solution. a. b. c. d. Q34. a. b. c. d. Q35. 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) Q36. 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) Q37. Solve the system of equations by elimination. a. x = 10, y = 0; (10, 0) b. x = 10, y = 10; (10, 10) c. x = 0, y = 10; (0, 10) d. x = 0, y = 0; (0, 0) Q38. The perimeter of a rectangle is 20 inches and its area is 21 square inches. What are its dimensions? a. 2 in. by 6 in. b. 3 in. by 7 in. c. 4 in. by 6 in. d. 2 in. by 8 in. Q39. Write the augmented matrix for the system. a. b. c. d. Q40. 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