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t 9. The equation for _____________ is y = C(1 – r) . ANSWER: exponential decay Study Guide and Review - Chapter 7 Choose the word or term that best completes each sentence. 4 n 10. If a = b for a positive integer n, then a is a(n) _______________ of b. 1. 7xy is an example of a(n)___________ . ANSWER: nth root ANSWER: monomial Simplify each expression. 3 5 11. x ⋅ x ⋅ x 5 2. The ___________ of 95,234 is 10 . ANSWER: ANSWER: order of magnitude x 3. 2 is a(n) __________ of 8. 9 2 5 12. (2xy)( −3x y ) ANSWER: cube root ANSWER: 3 6 −6x y 4. The rules for operations with exponents can be extended to apply to expressions with a(n) ___________ such as 4 . ANSWER: 6 6 ANSWER: rational exponent 20a b 3 2 2 14. (6x y ) n 5. A number written in is of the form a × 10 , where 1 ≤ a < 10 and n is an integer. ANSWER: 6 4 36x y ANSWER: scientific notation 3 3 2 15. [(2r t) ] x ANSWER: 6. f (x) = 3 is an example of a(n) ______________ . 18 6 64r t ANSWER: exponential function 7. 3 16. (−2u )(5u) is a(n) ANSWER: ______________ for the sequence . −10u ANSWER: = 16 is an example of a(n) 8. 2 _______________ . 8x ANSWER: exponential equation 9. The equation for _____________ is y = C(1 – r) . 15 3 3 18. t 10. If a = b for a positive integer n, then a is a(n) _______________ of b. 3 3 17. (2x ) (x ) 3x – 1 ANSWER: exponential decay 4 2 3 ANSWER: recursive formula eSolutionsnManual - Powered by Cognero 5 2 13. (−4ab )(−5a b ) (2x ) ANSWER: 4x 9 2 19. GEOMETRY Use the formula V = πr h to find the volume of the cylinder. Page 1 3 3 18. (2x ) ANSWER: ANSWER: Study Guide and Review - Chapter 7 9 4x 2 19. GEOMETRY Use the formula V = πr h to find the volume of the cylinder. 25. ANSWER: x ANSWER: 45πx 6 26. 4 ANSWER: 1 Simplify each expression. Assume that no denominator equals zero. 20. 27. ANSWER: ANSWER: 2 4 28. GEOMETRY The area of a rectangle is 25x y square feet. The width of the rectangle is 5xy feet. What is the length of the rectangle? 21. ANSWER: ANSWER: 3 5xy ft 22. Simplify. ANSWER: 4y 29. ANSWER: 7 −3 0 6 23. a b c ANSWER: 30. ANSWER: 3 24. 31. ANSWER: ANSWER: 5 32. 25. eSolutions Manual - Powered by Cognero ANSWER: 6 ANSWER: Page 2 40. 0.0000543 31. ANSWER: Study Guide and Review - Chapter 7 5 32. ANSWER: ANSWER: 5.43 × 10 −5 41. ASTRONOMY Earth has a diameter of about 8000 miles. Jupiter has a diameter of about 88,000 miles. Write in scientific notation the ratio of Earth’s diameter to Jupiter’s diameter. ANSWER: −2 about 9.1 × 10 33. ANSWER: 64 34. ANSWER: 4 Graph each function. Find the y-intercept, and state the domain and range. x 42. y = 2 ANSWER: 1; D = all real numbers; R = {y| y > 0} 35. ANSWER: 2401 36. ANSWER: x 43. y = 3 + 1 Solve each equation. x 37. 6 = 7776 ANSWER: 5 4x – 1 38. 4 ANSWER: 2; D = all real numbers; R = {y| y >1} = 32 ANSWER: Express each number in scientific notation. 39. 2,300,000 ANSWER: 6 2.3 × 10 40. 0.0000543 x 44. y = 4 + 2 ANSWER: 3; D = all real numbers; R = {y| y > 2} ANSWER: 5.43 × 10 −5 41. ASTRONOMY Earth has a diameter of about of about 88,000 miles. Write in scientific notation the ratio of Earth’s diameter to Jupiter’s diameter. eSolutions 8000Manual miles.- Powered Jupiter by hasCognero a diameter Page 3 47. Find the final value of $2500 invested at an interest rate of 2% compounded monthly for 10 years. Study Guide and Review - Chapter 7 x 44. y = 4 + 2 ANSWER: 3; D = all real numbers; R = {y| y > 2} ANSWER: $3053.00 48. COMPUTERS Zita’s computer is depreciating at a rate of 3% per year. She bought the computer for $1200. a. Write an equation to represent this situation. b. What will the computer’s value be after 5 years? ANSWER: t a. 1200(1 − 0.03) b. $1030.48 Find the next three terms in each geometric sequence. 49. −1, 1, −1, 1, ... ANSWER: −1, 1, −1 x 45. y = 2 − 3 ANSWER: −2; D = all real numbers; R = {y| y > −3} 50. 3, 9, 27 ... ANSWER: 81, 243, 729 51. 256, 128, 64, ... ANSWER: 32, 16, 8 Write the equation for the nth term of each geometric sequence. 52. −1, 1, −1, 1, ... ANSWER: n−1 46. BIOLOGY The population of bacteria in a petri dish increases according to the model p = 550(2.7) 0.008t , where t is the number of hours and t = 0 corresponds to 1:00 P.M. Use this model to estimate the number of bacteria in the dish at 5:00 P.M. a n = −1(−1) 53. 3, 9, 27, ... ANSWER: n−1 a n = 3(3) ANSWER: about 568 54. 256, 128, 64, ... 47. Find the final value of $2500 invested at an interest rate of 2% compounded monthly for 10 years. ANSWER: ANSWER: $3053.00 48. COMPUTERS Zita’s computer is depreciating at a rate of 3% per year. She bought the computer for $1200. a. Write an equation to represent this situation. b. What will the computer’s value be after 5 years? eSolutions Manual - Powered by Cognero ANSWER: t a. 1200(1 − 0.03) 55. SPORTS A basketball is dropped from a height of 20 feet. It bounces to its height each bounce. Draw a graph to represent the situation. ANSWER: Page 4 54. 256, 128, 64, ... ANSWER: Study Guide and Review - Chapter 7 55. SPORTS A basketball is dropped from a height of 20 feet. It bounces to its height each bounce. Draw a graph to represent the situation. ANSWER: Find the first five terms of each sequence. 56. ANSWER: 11, 7, 3, –1, –5 57. ANSWER: 3, 12, 30, 66, 138 Write a recursive formula for each sequence. 58. 2, 7, 12, 17, ... ANSWER: 59. 32, 16, 8, 4, ... ANSWER: 60. 2, 5, 11, 23, ... ANSWER: eSolutions Manual - Powered by Cognero Page 5