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Final Exam Study Guide 1 April 2019, questions and answers
Business Mathematics (Math 244)
Athabasca University
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2012 The Arizona Board of Regents For The University of Arizona All rights reserved Business Mathematics II Final Exam Study Guide NOTE: This final exam study guide contains a small sample of questions that pertain to mathematical and business related concepts covered in Math 115B. It is not meant to be the only final exam preparation resource. Students should consult their notes, homework assignments, quizzes, tests, and any other ancillary material so that they are well prepared for the final exam. Questions refer to the following data. Data representing the numbers of injury automobile accidents in the town during the past few years have been plotted on the graphs below. A logarithmic trend line and an exponential trend line have been used to model the data. Exponential Model Logarithmic Model y 2821(x) 154 0 0 0 2 4 6 8 Years after 1990 10 0 2 4 6 8 10 Years after 1990 Use the equation of the logarithmic trend line to predict the number of injury automobile accidents in the year 2002. The answer is: (A) (B) (C) (D) (E) 2. 0 1. y 2614.9e0 0 Number of Accidents Number of Accidents Less than Between and Between and Between and More than Use the equation of the exponential trend line to predict the number of injury automobile accidents in the year 2040. The answer is: (A) (B) (C) (D) (E) Less than Between and Between and Between and More than 3. In real world terms, explain why the prediction for the year 2040 given the exponential trend line is or is not reasonable. 4. Using the R 2 information provided in the graphs, which model would provide the better prediction for the number of injury automobile accidents in the years soon after (A) The logarithmic model because of the lower R 2 (B) The exponential model because of the higher R 2 (C) Since the R 2 is not used for making predictions, nothing can be determined regarding which model is the better predictor (D) There is not enough information to draw a conclusion 5. Suppose the demand function for manufacturing a telephone is 200 0 . If the fixed cost is and it costs to produce each telephone, determine the profit that could be made selling 500 telephones. (A) (B) (C) (D) (E) 6. If the demand function for a decorative vase is 2 0 450 , determine the price per unit that should be set in order to sell 700 vases. 9. A company that produces dining room tables determines that their fixed costs are and it will cost to produce each table. How many tables could be produced for a total cost of The total number of tables is: (A) (B) (C) (D) (E) Less than 900 Between 900 and 950 Between 950 and Between and 1050 More than 1050 Suppose the demand function for a certain product is given 2 80 . Use this function to answer questions 10 and 11. 10. Determine the largest possible quantity that could be produced using the demand function given above. (A) (B) (C) (D) (E) 11. 80 400 3578 17,889 Determine what should be inserted into the excerpt of Integrating shown below in order to plot 2 80 and estimate the total possible revenue. Definition Formula for f (x ) Computation f (x ) x Plot Interval A B Integration Interval a b b f ( x ) dx Use the graphs of profit and marginal profit to answer questions 12 and 13. Assume no more than 1400 units are produced and sold. Profit Marginal Profit 200 400 1200 1400 1600 Quantity On approximately what interval is C ? On approximately what interval is ? (A) (B) (C) (D) (E) 200 400 600 800 (A) (B) (C) (D) (E) 13. 800 12. 600 Dollars Dollars 0 Quantity 1200 1400 1600 19. The graphs of marginal revenue and marginal cost are show below. MR and MC 100 80 per unit 60 40 MR 20 MC 0 0 20 40 60 80 100 120 140 160 Quantity Use the graphs to determine whether revenue, cost, and profit are increasing, decreasing, or constant at a quantity of 100 units. (A) Revenue: Decreasing Cost: Constant Profit: Decreasing (B) Revenue: Increasing Cost: Increasing Profit: Decreasing (C) Revenue: Increasing Cost: Constant Profit: Decreasing (D) Revenue: Increasing Cost: Increasing Profit: Increasing (E) Revenue: Decreasing Cost: Decreasing Profit: Increasing 20. The demand function for a product is 2 60 . Use a difference quotient with h 0 to estimate the marginal demand when 5 units are produced. (A) per unit (B) per unit (D) per unit (E) per unit (C) per unit 21. 22. A company that produces mirrors for telescopes estimates the values for the following functions when 1200 mirrors are produced: , C , , and . Due to a change in the economy, the revenue function decreased and cost increased Determine the revenue, cost, marginal revenue, and marginal cost under the new economic conditions if 1200 mirrors are produced. The cost for producing a new type of sunglasses is given 70q . An investment of for new equipment would decrease marginal costs Determine a formula for the new cost function and new marginal cost function. (A) 70q MC 70 (B) 10 10 (C) 70q 59 (D) 70q MC 70 (E) 59 59 23. Let f f is: (A) (B) (C) (D) (E) 24. 5x . Use a difference quotient with h to approximate f . The value of x Less than Between and Between and 0 Between 0 and 1 More than 1 Let g 0 x 2 . Use a difference quotient with h 0 to approximate g . Round your answer to 4 decimal places. 29. Graphs of y k and the tangent line to the graph of y k at x 1 are given below. 6 5 4 3 2 1 0 0 1 2 3 4 5 6 Use the graphs to determine k . (A) 0 30. (B) 1 3 (C) 1 (D) 3 (E) None of the above Let represent the price (in dollars per watch) at which q watches can be sold. Give a practical interpretation of 320 . (A) (B) (C) (D) When 200 watches have been manufactured, the price per watch should be The price for 200 watches is For every 200 watches manufactured, the price increases per watch. When 200 watches have been manufactured, the price increases when one more watch is manufactured. (E) When 320 watches have been manufactured, the price per watch should be 31. Let represent the price (in dollars per watch) at which q watches can be sold. Give a practical interpretation of . When 200 watches have been manufactured, the price per watch should be For every 200 watches manufactured, the price decreases per watch. For every 200 watches manufactured, the price increases per watch. When 200 watches have been manufactured, the price decreases when one more watch is manufactured. (E) When 200 watches have been manufactured, the price increases when one more watch is manufactured. (A) (B) (C) (D) 32. Fill in the boxes of the screen capture in such a way that Solver would find a value for q so that is equal to 34. Fill in the boxes of the screen capture in such a way that Solver would find a value for q which gives a maximum value for using a reference to the marginal profit. Consider the function f 2 x 5 3x 2 15 on the interval 2, . Use this function to answer questions which relate to the steps for calculating the midpoint sum S 4 f , 2, . 35. Use the interval given above to determine the x0 , x1 , x2 , x3 , and x4 that divide the interval 2, into four subintervals of equal length. (A) (B) (C) (D) (E) 36. x1 x1 x1 x1 x1 What is the value of x1 ? 0 0 Use the information given above to determine the midpoints m1 , m2 , m3 , and m4 of the four subintervals. What is the value of m3 ? (A) m3 0 (B) m3 (C) m3 (D) m3 (E) m3 37. Use the information given above to determine the function value at each of the midpoints of the four subintervals. What is the value of f ? Round to 4 decimal places if necessary. (A) (B) (C) (D) (E) 38. f 10 f 14 f 14 f 14 f 15 Use the information given above to determine the midpoint sum S 4 f , 2, . Round to 4 decimal places if necessary. (A) (B) (C) (D) (E) 2 4 Cannot be determined 41. (Project 1) Data representing the costs for producing the UDMA CompactFlash cards for Project 1 are provided in the table below. Fixed Cost For The Year (in millions) Variable Costs Quantity (in thousands) First 400 Next 700 Further: Cost per unit Determine the total cost for producing units. (A) (B) (C) (D) (E) 42. (Project 1) Which of the following functions can be negative? (A) (B) (C) (D) (E) 43. million million million million None of these Demand Revenue Cost Marginal Revenue Marginal Cost (Project 1) Suppose the demand function for producing the UDMA CompactFlash cards for Project 1 is 2 0 510 . Determine a formula for marginal revenue, , using the properties for derivatives. (A) (B) (C) (D) (E) 0 2 0 510 2 0 2 0 510 2 0 44. (Project 1) Data representing the costs for producing the UDMA CompactFlash cards for Project 1 are provided in the table below. Fixed Cost For The Year (in millions) Variable Costs Quantity (in thousands) First 400 Next 700 Further: Cost per unit What is the marginal cost when units have been manufactured? (A) (B) (C) (D) (E) per unit per unit per unit per unit Cannot be determined 46. The p.m. values for a finite random variable T are listed in the table below. t 3 12 f T 0 0 0 0 Determine the mean of T, T . (A) (B) (C) (D) (E) 6 2 1 1 0 Use the following information to answer questions Let W be a binomial random variable with parameters n 20 and p 0 . A screen capture of BINOMDIST function is given below. 47. Which of the following formulas would compute ? (A) (B) (C) (D) (E) BINOMDIST(4, 20, 0, TRUE) 1 BINOMDIST(4, 20, 0, TRUE) BINOMDIST(4, 20, 0, FALSE) 1 BINOMDIST(4, 20, 0, FALSE) BINOMDIST(5, 20, 0, TRUE) 48. Which of the following formulas would compute ? (A) (B) (C) (D) (E) 49. BINOMDIST(4, 20, 0, TRUE) 1 BINOMDIST(4, 20, 0, TRUE) BINOMDIST(4, 20, 0, FALSE) 1 BINOMDIST(4, 20, 0, FALSE) BINOMDIST(5, 20, 0, TRUE) Determine the mean of W, . Round to 4 decimal places if necessary. (A) (B) (C) (D) (E) 10 2 1 1 1
Final Exam Study Guide 1 April 2019, questions and answers
Course: Business Mathematics (Math 244)
University: Athabasca University
