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Name ________________________________________ Date __________________ Class __________________ Exponential Relationships UNIT 6 Practice Test 1. Which exponential function matches the values in the table below? x 1 2 3 f(x) −18 162 −1458 A f(x) = 6. Does each set of ordered pairs satisfy an exponential function? A {(1, 2), (2, 6), (3, 18), (4, 54)} Yes 1 (−18)x 2 No B {(1, −2), (2, 4), (3, −6), (4, 8)} B f(x) = 2(−9)x Yes C f(x) = −2(3)2x No C {(−2, 1), (−8, 2), (−32, 3), (−128, 4)} D f(x) = −18x 2. What are the next two terms in the sequence −9, 3, −1, …? Yes No D {(−1, 2), (0, −10), (1, 50), (2, −250)} ________________________________________ Yes 3. The first term of a geometric sequence is −10 and the common ratio is 4. Write the explict rule of the sequence and find the fifth term of the sequence. No For 7–9, solve for x. 7. 2 x 6 = 864 3 ________________________________________ ________________________________________ 8. 6(7)x = 2058 ________________________________________ ________________________________________ 4. Write an equation for an exponential function that includes the points (3, 18) and (4, 54). x 3⎛5⎞ 125 9. ⎜ ⎟ = 5⎝9⎠ 2187 ________________________________________ 10. A new movie premiered on Friday, September 2, and 1350 people attended. Attendance then decreased by 20% each day. Write an exponential decay function to model this situation. Then find the attendance on September 7. ________________________________________ 5. Which of the following regression equations could represent a town with an initial population of 875 people and an annual growth rate of approximately 2%? A y = 875 i 1.02x B y = 875(1.02)x C y = 875(2) ________________________________________ x ________________________________________ D y = 875x1.02 Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 1 Name ________________________________________ Date __________________ Class __________________ UNIT 6 Exponential Relationships Practice Test 11. a. Graph y = 3x and y = 3x + 4. 13. Use the parent function f(x) = 2.5x. a. Complete the table. f(x) = 0.5(2.5)x x −2 −1 0 1 2 x b. Compare the graphs of y = 3 and y = 3x + 4. b. Add the graph of the translation to the graph of the parent function. ____________________________________ ____________________________________ ____________________________________ ____________________________________ 12. Alistair has $900 in his savings account. He is looking at two investment plans. Under Plan A, he will increase his account balance by $250 a year. Under Plan B, he will increase his account balance by 25% each year. c. Describe the end behavior and find the y-intercept of the new graph. ____________________________________ 14. The table shows the population y of a town over a period of time. a. Write equations to represent the money Alistair would have under Plan A and Plan B. ____________________________________ ____________________________________ b. To the nearest penny, how much more under Plan B would Alistair save than under Plan A after 5 years? Year Population 0 6915 1 2 7285 7780 3 8293 4 8701 5 9284 6 9816 Write an exponential regression function for the data. Round to the nearest hundredth. ____________________________________ _________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 2 Name ________________________________________ Date __________________ Class __________________ UNIT 6 Exponential Relationships Practice Test 17. The drama club had a car wash as a fundraiser. Members washed and total of 11 vehicles charging cars $5 each and trucks $8 each. They made $250. Find the number of each type of vehicle they washed during the car wash using a systems of equations. 15. Ben has $100 in his savings account. He is looking at two investment plans. Under Plan A, he will increase his account balance by $20 a year. Under Plan B, he will increase his account balance by 15% each year. Approximately how much will Ben save after 3 years with each plan? _________________________________ ________________________________________ ________________________________________ 19. Travis has $60 in dimes and quarters. If he could switch the numbers of dimes with the number of quarters, he would have $87. How many of each coin does Travis have using a systems of equations? 16. Ashley is deciding between two jobs. Job A pays $2000 per month with a monthly raise of $85. Job B pays $2000 per month with a monthly raise of 4%. a. Write a function to represent the monthly salary for Job A. ____________________________________ b. Write a function to represent the monthly salary for Job B. ____________________________________ c. After how many months would Ashley have a greater salary at Job B? _________________________________ 20. Lewis checked the balance of his savings account every month for 4 months. The balances were $300, $410, $520, and $630. Would a linear or exponential function better represent the data? Explain. ________________________________________ ________________________________________ ____________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 3