Class: Date: Algebra II Quiz: Lessons 7.1 through 7.4 Review Graph: 1. f( x) = 4 x 1
2. Graph the function: f( x) = 3 x 2
a. b. 3
c. d. 3. Find the y-intercept of the equation. y = 3 7 x a. 4 b. 21 c. 3 d. 7 4. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound annual rate, r, is given by A = P(1 + r) n. If a person invests $250 in an account that pays 10% interest compounded annually, find the balance after 15 years. 4
5. The amount of money, A, accrued at the end of n years when a certain amount, P, is invested at a compound annual rate, r, is given by A =P( 1+r) n. If a person invests $310 in an account that pays 8% interest compounded annually, find the balance after 5 years. a. $455 b. $2790 c. $13,950 d. $443 6. The projected worth (in millions of dollars) of a large company is modeled by the equation y = 256( 1.04) x. The variable x represents the number of years since 1997. What is the projected annual percent of growth, and what should the company be worth be in 2007? 7. The projected worth (in millions of dollars) of a large company is modeled by the equation y = 241( 1.04). The variable x represents the number of years since 1997. What is the projected annual percent of growth, and what should the company be worth in 2001? a. 14%; $293.21 million c. 14%; $250.64 million b. 4%; $271.09 million d. 4%; $281.94 million 8. Find the value of $1000 deposited for 8 years in an account paying 8% annual interest compounded semiannually. 9. How much money must be deposited now in an account paying 7% annual interest, compounded yearly, to have a balance of $1000 after 6 years? 10. Sara bought 6 fish. Every month the number of fish she has doubles. After m months she will have F fish, where F = 6 2 m. How many fish will Sara have after 2 months if she keeps all of them and the fish stay healthy? a. 20 b. 10 c. 144 d. 24 11. If there are initially 4000 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours can be found using the formula N = 4000 Ê 2 t ˆ Ë Á. How many bacteria will be present after 9 hours? a. 2,048,000 b. 4,096,000 c. 1,024,000 d. 72,000 5
Ê 12. Graph the function: f( x) = 1 ˆ Ë Á 4 x 6
a. b. 7
c. d. 13. Describe y=2.9 x as an example of exponential growth or exponential decay. 8
Graph: Ê 14. f(x) = 2 1 ˆ Ë Á 4 x a. c. b. d. Writing: 15. How does changing the value of b affect the graph of an exponential equation of the form y = ab x? Simplify: 16. 7e 19 35e 6 a. 5e 25 c. 5e 13 1 b. 5 e 13 1 d. 5 e 25 Simplify the expression. 17. e x 6e 3x 1 9
18. Graph f( x) = 3 + e x. a. c. b. d. 19. Is f( x) = 13.7e 0.04t an example of exponential growth or decay? 20. Sketch the graph of the function. f( x) = 1 3 e x 2 21. If $2500 is invested at a rate of 11% compounded continuously, find the balance in the account after 4 years. Use the formula A =Pe rt. a. $3795.18 b. $3881.77 c. $4333.13 d. $18472.64 22. The formula A = 2000e rt can be used to find the dollar value of an investment of $2000 after t years when the interest is compounded continuously at a rate of r percent. Find the value of the investment after 6 years if the interest rate is 7%. Find the value of the investment after 12 years if the interest rate is 8%. a. $3043.92; $2920.47 c. $3043.92; $5223.39 b. $4901.85; $5223.39 d. $4901.85; $2920.47 True or False: 23. The formula for interest compounded continuously is A = Pe t. 24. The formula for interest compounded continuously is A = Pe rt. 10
Evaluate: 25. log 3 729 1 a. 6 b. 18 c. 6 d. 1 18 26. Graph the function y = 1.2 x and its reflection over the line y = x. Is the reflection the graph of a function? a. c. No No b. d. Yes Yes 11
Graph: 27. y = log 3 x a. c. b. d. 28. Use the formula R = log 10 I, where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 53,000,000. a. 7.7243 b. 1.77858 c. 0.77243 d. 17.7858 29. Evaluate ln e 4. Graph the function. State the domain and range. 30. y = ln( x + 2) 12
Algebra II Quiz: Lessons 7.1 through 7.4 Review Answer Section 1. ANS: PTS: 1 DIF: Level B REF: MAL21000 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: function graph exponent BLM: Knowledge NOT: 978-0-618-65615-8 2. ANS: B PTS: 1 DIF: Level B REF: MAL21002 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: function graph exponential BLM: Knowledge NOT: 978-0-618-65615-8 3. ANS: C PTS: 1 DIF: Level B REF: MAL21004 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: exponential equation BLM: Knowledge NOT: 978-0-618-65615-8 4. ANS: $1044 PTS: 1 DIF: Level B REF: MAL21006 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 MI.MIGLC.MTH.06.9-12.A1.2.9 MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word log compound interest BLM: Application NOT: 978-0-618-65615-8 5. ANS: A PTS: 1 DIF: Level B REF: MAL21007 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 MI.MIGLC.MTH.06.9-12.A1.2.9 MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word log compound interest BLM: Application NOT: 978-0-618-65615-8 6. ANS: 4%; $378.94 million PTS: 1 DIF: Level B REF: MAL21008 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word exponential growth BLM: Application NOT: 978-0-618-65615-8 7. ANS: D PTS: 1 DIF: Level B REF: MAL21009 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word exponential growth BLM: Application NOT: 978-0-618-65615-8 1
8. ANS: $1872.98 PTS: 1 DIF: Level A REF: MAL21014 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 MI.MIGLC.MTH.06.9-12.A1.2.9 MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: compound interest BLM: Application NOT: 978-0-618-65615-8 9. ANS: $666.34 PTS: 1 DIF: Level B REF: MAL21017 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 MI.MIGLC.MTH.06.9-12.A1.2.9 MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: compound interest BLM: Application NOT: 978-0-618-65615-8 10. ANS: D PTS: 1 DIF: Level B REF: MAL21020 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: law of exponents word BLM: Application NOT: 978-0-618-65615-8 11. ANS: A PTS: 1 DIF: Level B REF: MAL21022 TOP: Lesson 7.1 Graph Exponential Growth Functions KEY: word exponential growth BLM: Application NOT: 978-0-618-65615-8 12. ANS: C PTS: 1 DIF: Level B REF: MAL21028 TOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph function BLM: Knowledge NOT: 978-0-618-65615-8 13. ANS: exponential growth PTS: 1 DIF: Level B REF: MAL21029 NAT: NCTM 9-12.ALG.1.c STA: MI.MIGLC.MTH.06.9-12.A2.5.2 TOP: Lesson 7.2 Graph Exponential Decay Functions KEY: exponential growth exponential decay BLM: Comprehension NOT: 978-0-618-65615-8 14. ANS: D PTS: 1 DIF: Level B REF: MAL21031 TOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph exponential function BLM: Knowledge NOT: 978-0-618-65615-8 15. ANS: Sample answer: For b > 0, as the value of b increases, the curve slopes upward faster; that is, the value of y increases at a faster rate. For 0 < b < 1, as the value of b increases, the curve slopes downward slower; that is, the value of y decreases at a slower rate. PTS: 1 DIF: Level B REF: MAL21032 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 7.2 Graph Exponential Decay Functions KEY: graph exponential BLM: Analysis NOT: 978-0-618-65615-8 16. ANS: B PTS: 1 DIF: Level B REF: MAL21041 TOP: Lesson 7.3 Use Functions Involving e KEY: exponent exponential rules simplify BLM: Comprehension NOT: 978-0-618-65615-8 2
17. ANS: 6e 4x 1 PTS: 1 DIF: Level B REF: MAL21042 TOP: Lesson 7.3 Use Functions Involving e KEY: exponent multiply e BLM: Comprehension NOT: 978-0-618-65615-8 18. ANS: D PTS: 1 DIF: Level B REF: MAL21049 TOP: Lesson 7.3 Use Functions Involving e KEY: function graph exponential BLM: Knowledge NOT: 978-0-618-65615-8 19. ANS: Decay PTS: 1 DIF: Level A REF: MAL21052 STA: MI.MIGLC.MTH.06.9-12.A2.5.2 TOP: Lesson 7.3 Use Functions Involving e KEY: function exponential growth exponential decay BLM: Knowledge NOT: 978-0-618-65615-8 20. ANS: PTS: 1 DIF: Level B REF: MAL21053 TOP: Lesson 7.3 Use Functions Involving e KEY: graph exponential function e BLM: Comprehension NOT: 978-0-618-65615-8 21. ANS: B PTS: 1 DIF: Level B REF: MAL21058 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 MI.MIGLC.MTH.06.9-12.A1.2.9 MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.3 Use Functions Involving e KEY: word interest compound continuous BLM: Application NOT: 978-0-618-65615-8 22. ANS: C PTS: 1 DIF: Level B REF: MAL21060 STA: MI.MIGLC.MTH.06.9-12.L2.2.3 MI.MIGLC.MTH.06.9-12.A1.2.9 MI.MIGLC.MTH.06.9-12.A3.1.1 TOP: Lesson 7.3 Use Functions Involving e KEY: interest continuous compounded continuously BLM: Application NOT: 978-0-618-65615-8 3
23. ANS: False PTS: 1 DIF: Level B REF: MAL21062 TOP: Lesson 7.3 Use Functions Involving e KEY: word interest e compounded continuously NOT: 978-0-618-65615-8 24. ANS: True BLM: Comprehension PTS: 1 DIF: Level B REF: MAL21063 TOP: Lesson 7.3 Use Functions Involving e KEY: e compounded continuously word interest BLM: Comprehension NOT: 978-0-618-65615-8 25. ANS: C PTS: 1 DIF: Level A REF: MAL21066 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic Functions KEY: log evaluate exponential BLM: Knowledge NOT: 978-0-618-65615-8 26. ANS: B PTS: 1 DIF: Level B REF: MAL21076 NAT: NCTM 9-12.GEO.3.a TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic Functions KEY: graph exponential inverse function BLM: Comprehension NOT: 978-0-618-65615-8 27. ANS: C PTS: 1 DIF: Level B REF: MAL21081 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic Functions KEY: log graph BLM: Comprehension NOT: 978-0-618-65615-8 28. ANS: A PTS: 1 DIF: Level B REF: MAL21110 STA: MI.MIGLC.MTH.06.9-12.A1.2.7 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic Functions KEY: logarithms word BLM: Application NOT: 978-0-618-65615-8 29. ANS: -4 PTS: 1 DIF: Level B REF: MAL21073 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic Functions KEY: logarithm e BLM: Knowledge NOT: 978-0-618-65615-8 4
30. ANS: Domain: x > 2; Range: all real numbers PTS: 1 DIF: Level B REF: MAL21089 NAT: NCTM 9-12.ALG.1.c STA: MI.MIGLC.MTH.06.9-12.A2.5.2 TOP: Lesson 7.4 Evaluate Logarithms and Graph Logarithmic Functions KEY: log graph BLM: Comprehension NOT: 978-0-618-65615-8 5