Q1. Find the exact value of the logarithmic expression log ₄ 1/64.
   a. -1/3
   b. -3
   c. 1/3
   d. 3

Q2. Solve the equation log ₇₂ (x² - x) = 1.
   a. {-8, -9}
   b. {1, 72}
   c. {8, 9}
   d. {-8, 9}

Q3. 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}

Q4. 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

Q5. 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

Q6. Solve the equation log ₄ (x + 4) + log ₄ (x - 2) = 2
   a. {-6}
   b. {4}
   c. {4, -6}
   d. {5}

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. 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.

Q9. 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

Q10. If f(x) = 4^x 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)

Q11. A thermometer reading 8°C is brought into a room with a constant temperature of 20°C. If the thermometer reads 18°C 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)e^kt. (Round your answer to two decimal places.)
   a. 1.6°C
   b. 20.98°C
   c. 19.02°C
   d. 20°C

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 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

Q14. 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

Q15. Solve the equation 8^{x - 4} = 32^4x.
   a. {-12/17}
   b. {-4/3}
   c. {-2}
   d. {-4/17}

Q16. Solve the equation log ₄ (x + 2) = -1
   a. {-7}
   b. {-7/4}
   c. {9/4}
   d. {9}

Q17. Find the exact value of the logarithmic expression ln e.
   a. 0
   b. -1
   c. 1
   d. e

Q18. Use the horizontal line test to determine whether the function is one-to-one.


   a. Yes
   b. No

Q19. Find the present value to get $6500 after 2 years at 5% compounded quarterly. Round to the nearest cent.
   a. $5895.69
   b. $614.91
   c. $5885.09
   d. $5958.65

Q20. Solve the equation 3^{(1 + 2x)} = 243.
   a. {81}
   b. {2}
   c. {-2}
   d. {6}

Q21. 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)

Q22. Write the partial fraction decomposition of the rational expression x/(x² - 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)

Q23. 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)

Q24. Graph the inequality x + y < -5.
   a.
   b.
   c.
   d.

Q25. 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.

Q26. Perform the row operations on the given augmented matrix.


   a.
   b.
   c.
   d.

Q27. 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)

Q28. Write the partial fraction decomposition of the rational expression (4x³ + 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

Q29.
   a.
   b.
   c.
   d.

Q30. Solve the system using the inverse matrix method.


   a. x = -33, y = 51, z = -26; (-33, 51, -26)
   b. x = -31, y = -29, z = -6; (-31, -29, -6)
   c. x = -36, y = 16, z = 10; (-36, 16, 10)
   d. x = 1, y = 24, z = -35; (1, 24, -35)

Q31. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
   a. minimum: 7
   b. minimum: 18
   c. minimum: 24
   d. minimum: 13

Q32. 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)

Q33. 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

Q34.
   a.
   b.
   c.
   d.

Q35.
   a.
   b.
   c.
   d.

Q36. 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.

Q37. A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and an ounce of potatoes for $0.03. Let x = the number of ounces of chicken and y = the number of ounces of potatoes purchased per patient. Write the objective function that describes the total cost per patient per meal.
   a. z = 3y + 25y
   b. z = 0.25x + 0.03y
   c. z = 25x + 3y
   d. z = 0.03x + 0.25y

Q38. 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

Q39. Find the inverse of the matrix. Be sure to check your answer.


   a.
   b.
   c.
   d.

Q40. Write the system of equations associated with the augmented matrix. Do not solve.


   a.
   b.
   c.