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H-Algebra II Name _____________________________ Chapter 7 Targets Chapter Objective: To graph, evaluate, and solve exponential and logarithmic functions, to expand and condense logarithmic expressions, and to write equations for exponential and power functions. 7.1/7.2 Exponential Growth and Decay Functions I can graph For #1-3, GRAPH each and state the DOMAIN and RANGE. exponential growth functions and state 1 x x 2 x 1 1. y 4 2. y2 3 3. y 23 4 domain and range. 2 I can graph For #4-6, GRAPH each and state the DOMAIN and RANGE. exponential decay x x 1 x 2 functions and state 1 2 1 4. y 3 5. y 6 3 6. y 2 5 domain and range. 2 3 4 I can determine if For #7-8, determine if each function shows growth or decay. Explain. an exponential x x function shows 37 2 7. y 8. y 3 growth or decay. 45 5 9. How much must you deposit into an account that pays 7.45% interest, compounded weekly, to have a balance of $35,000 after 10 years? I can use exponential 10. What is the interest rate on an account that is compounded monthly for 8 functions to model years, to have a balance of $12,000 from an initial deposit of $9,000? and solve problems. 11. The population of Z-ville is currently 50,000. If 7% of the population leaves the town each year, what will be the population after 10 years? 7.3 Functions involving e I can simplify 2 9 4 34 16e e natural base 12. Simplify e e 13. Simplify 7 expressions. 6e I can graph natural For #14-16, GRAPH each and state the DOMAIN and RANGE. base functions and state domain 1 x x 2 x 1 14. y e 15. y e 3 16. y 2e 4 and range. 2 I can determine if a For #17-18, determine if each function shows growth or decay. Explain. natural base function shows 2x 1 x 3 17. y 2e 18. y 3e growth or decay. 19. If an account earning 2.45% interest, compounded continuously, currently I can use natural has $5,000 after being deposited 4 years ago, what was the initial deposit? base functions to model and solve 20. For a certain strain of bacteria, k = 0.672 when t is measured in hours. problems. How long will it take 250 bacteria to increase to 700 bacteria? 7.4 Evaluate and Graph Logarithms I can rewrite For #21-23, rewrite in exponential form. logarithmic equations 1 21. log3 81 4 3 23. log4 2 in exponential form. 22. log4 8 2 16 I can evaluate For #24-27, evaluate each WITHOUT A CALCULATOR! logarithmic 1 expressions. 24. log4 64 25. log2 1 26. log25 5 27. log2 8 For #28-29, find the inverse of the given function. I can find the inverse of exponential and logarithmic functions. 28. y5 x 2 1 29. y 3log6 x 2 1 I can graph For #30-32, GRAPH each and state the DOMAIN and RANGE. logarithmic functions and state domain 30. y 3•log2 x 31. y ln x 2 3 32. y 2log x 3 4 and range. 7.5 Apply Properties of Logarithms For #33-34, expand each expression. I can expand 3 2 logarithmic 6 2 x y expressions. 33. log7 3x y 34. ln 4z I can condense For #35-36, condense each expression. logarithmic 1 expressions. 35. 4log3 x 2log3 y 7log3 a log3 b 36. 3ln x 5ln y 2lnz 2 I can use the change For #37-40, use the change of base to evaluate each. of base to evaluate 37. log5 7 38. log3 12 39. log6 2 40. log3 0.25 logarithms. 7.6 Exponential and Logarithmic Equations For #41-44, solve for x. I can solve x 10 exponential 41. 9 2 5 42. 15.47 14.1e 2x 9 equations. 4x 5 x 2 3x 1 2x 3 43. 10 6 44. 5 2 For #45-52, solve for x. 45. log5 x 4 log510 46. log3x 9 3 I can solve 47. log10 log2 log7 x 0 1 48. logx 3 49 logarithmic 3 equations. 1 2 49. log3 9 log3x log3 72 50. 2log9 x log9 144 log9 8 2 3 2 51. log2 9x 5 log2 x 1 2 52. log2 y 2 1 log2 y 2 7.7 Write Exponential Functions x I can write an 53. Write an exponential function y ab through (1, 40) and (3, 640). exponential/power function. b 54. Write a power function y ax through (5, 10) and (12, 81) x I can find an 55. Write an exponential function y ab whose graph passes through the exponential or power points {(1, 3.3), (2, 10.1), (3, 30.6), (4, 92.7), (5, 280.9)} function from a set of data (use a b graphing calculator). 56. Write a power function y ax whose graph passes through the points {(1, 2), (2, 5), (3, 10), (4, 15), (5, 22)}