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Name: ______________________ Class: __________________ AU6 – Exponents & Exponential Review Total: 54 pts Multiple Choice Circle the choice that best completes the statement or answers the question. (2 pts each) 1. What is the value of 4 2 4 0 ? a) 0 b) 1 c) 1 16 d) 1 1 16 2. Write the following using the appropriate unit in prefix form. 2.8 10 3 meters a) 2.8 centimeters b) 0.28 millimeters c) 2.8 kilometers d) 2800 kilometers c) 9 7 d) 3 7 3. The expression 33 3 4 is equivalent to a) 9 12 b) 312 4. Which expression represents 3x 2 y 4 4 xy2 in simplest form? a) 12 x 2 y 8 b) 12 x 2 y 6 c) 12 x 3 y 8 d) 12 x 3 y 6 c) 27x 5 d) 27x 6 5. The expression (3x 2 ) 3 is equivalent to a) 9x 5 b) 9x 6 3x 6 x in simplest form? 2 4 6. Which expression represents a) 9x 9x b) 2x c) x 9 d) 2x 3 c) 6 3 3 2 d) 3 2 36 7. The expression 9 3 2 3 is equivalent to a) 3 6 2 3 b) 6 3 2 3 1 8. What is the approximate solution to the given system? f x 2 x g x 4 x 10 a) 1.69, 3.23 b) 1.67, 3.33 d) 3.23, 1.69 c) No solution 9. Which of the following functions model an exponential decay? a) f x x 4 b) g x 2 4 c) h( x) x x 1 d) j x 2 4 2 x 10. Which equation best represents the data in the accompanying table? 1 a) y 3 x y 1 3 2 9 3 27 4 81 x b) y 3 x d) y x 3 c) y 3 x 11. Kathy plans to purchase a car that depreciates (loses value) at a rate of 14% per year. The initial cost of the car is $21,000. Which equation represents the value, v of the car after 3 years? a) v 210000.14 3 b) v 210000.86 3 c) v 210001.14 12. Which statement about this sequence is true? 5, -25, 125, -625, … a) The sequence is not geometric and the common ratio is -5. b) The sequence is arithmetic and the common difference is -5. c) The sequence is geometric and the common ratio is 5. d) The sequence is geometric and the common ratio is -5. 2 3 d) v 210001.86 3 Short Answer: 13. Find the product of 2.5 10 5 and 4 10 3 . Leave your answer in scientific notation. (2pts) 14. Evaluate the expression 4 x 3 y for x 2 and y 5 . 15. Simplify the following: 3.6 10 7 . Leave your answer in scientific notation. 3 10 3 16. Suppose a population of 150 mice triples in size every 4 months. How many mice will there be after 3 years? 3 (2pts) (2pts) (2pts) 17. The inside diameter of a certain size of ring is 1.732 10 2 meter. Is it more appropriate to report the ring diameter as 1.732 10 2 meter or 17.32 millimeters? Explain. (2pts) ________________________________________________________________________ ________________________________________________________________________ 18. Is the statement 0.25 4 1 true or false? Explain your reasoning. (2pts) ________________________________________________________________________ ________________________________________________________________________ 19. The population of the District of Columbia (D.C.) is about 5.9 10 5 . South Dakota has a population of approximately 8 10 5 . a. Find the total of the populations. Leave your answer in scientific notation. b. How many more people live in South Dakota than in D.C.? Leave your answer in scientific notation. 4 (2pts) 20. If a new car cost $25,000 and the rate of depreciation is 8% per year. (3pts) a. Write an equation that models the cost of a new car. b. Use your equation to determine what the value of the car is after 60 months, round to the nearest cent. 21. Chain emails are emails with a message suggesting you will have good luck if you forward the email on to others. Suppose a student started a chain email by sending the message to 3 friends and asking those friends to each send the same email to 3 more friends exactly 1 day after they received it. (3pts) a. Write an explicit formula for the sequence that models the number of people who will receive the email on the nth day. (Let the first day be the day the original email was sent.) Assume everyone who receives the email follows the directions. b. Which day will be the first day that the number of people receiving the email exceeds 100? 5 22. On the set of axes below, solve the following system of equations graphically for all values of x and y. (4 pts) y 0.5 4 x y 60 x 112 y x 6 23. Population of Smallville Year Population in thousands (6 pts) 2007 2008 2009 2010 2011 2012 15 17.6 22.2 28.7 49.3 37.1 a. Use the statistical features of your calculator to construct a scatter plot and fit an appropriate function to the data. Justify using the correlation coefficient. b. From your table, calculate the average rate of change in total number of sightings for each of the following time intervals. a. 2007–2009 b. 2009–2011 c. How do the average rates of change help to support your argument of whether a linear or exponential model is better suited for the data? 7