C Challenge

52. The function S ( n ) = 10 ( 1 − 0.8 n ) 0.2 s , open n close , equals . fraction 10 . open . 1 minus , 0.8 to the n . close , over 0.2 end fraction  represents the sum of the first n terms of an infinite geometric series.
    1. What is the domain of the function?
    2. Find S ( n ) s open n close  for n = 1 , 2 , 3 , … , 10 . n equals 1 , comma 2 comma 3 comma dot dot dot comma 10 .  Sketch the graph of the function.
    3. Find the sum S of the infinite geometric series.
53. Use the formula for the sum of an infinite geometric series to show that 0. 9 ¯ = 1 . 0. , 9 bar , equals 1 .  (Hint: 0. 9 ¯ = 9 10 + 9 100 + 9 1000 = … 0. , 9 bar , equals , 9 tenths , plus , 9 100ths , plus , 9 over 1000 , equals dot dot dot )

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

54. What is the value of ∑ n = 1 5 ( 2 n − 3 ) ? sum , from , n equals 1 , to , 5 , of . open , 2 n minus 3 , close . question mark
55. Evaluate the infinite geometric series 2 5 + 4 25 + 8 125 + … . 2 fifths , plus , 4 twenty fifths , plus , 8 over 125 , plus dot dot dot .  Enter your answer as a fraction.
56. Use log 5 2 ≈ 0.43 log base 5 , 2 almost equal to , 0.43  and log 5 7 ≈ 1.21 log base 5 , 7 almost equal to , 1.21  and the properties of logarithms to approximate log 5 14 log base 5 , square root of 14  without using a calculator.
57. Use a calculator to solve the equation 7 2 x = 75 . 7 super 2 x end super , equals 75 .  Round the answer to the nearest hundredth.
58. Use the Change of Base Formula and a calculator to solve log 9 x = log 6 15 . log base 9 , x equals , log base 6 , 15 .  Round the answer to the nearest tenth.

Mixed Review

See Lesson 9-4.

Evaluate each series to the given term.

59. 12 . 5 + 15 + 17 . 5 + 20 + 22 . 5 + … ; 12 . 5 plus 15 plus 17 . 5 plus 20 plus 22 . 5 plus dot dot dot semicolon  7th term
60. − 100 − 95 − 90 − 85 − … ; negative 100 minus . 95 minus 90 minus 85 . minus dot dot dot semicolon  11th term

See Lesson 8-5.

Add or subtract. Simplify where possible.

61. 7 2 c − 2 c 2 fraction 7 , over 2 c end fraction , minus , fraction 2 , over c squared end fraction
62. 5 y + 3 + 15 y − 3 fraction 5 , over y plus 3 end fraction . plus . fraction 15 , over y minus 3 end fraction
63. 4 x 2 − 36 + x x − 6 fraction 4 , over x squared , minus 36 end fraction . plus . fraction x , over x minus 6 end fraction

See Lesson 7-4.

Use the properties of logarithms to evaluate each expression.

64. log 2 1 8 + log 2 8 log base 2 . 1 eighth , plus , log base 2 , 8
65. log 15 25 + log 15 9 log base 15 , 25 plus , log base 15 , 9
66. 3 log 9 3 − 1 4 log 9 81 3 , log base 9 , 3 minus , 1 fourth . log base 9 , 81

Get Ready! To prepare for Lesson 10-1, do Exercises 67–69.

See Lesson 4-2.

Graph each function.

67. y = x 2 − 4 y equals . x squared , minus 4
68. y = x 2 − 6 x − 9 y equals . x squared , minus , 6 x minus 9
69. y = − 4 x 2 + 1 y equals minus . 4 x squared , plus 1

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