Standardized Test Prep

SAT/ACT

45. A savings account earns 4.62% annual interest, compounded continuously. After approximately how many years will a principal of $500 double?
    1. 2 years
    2. 10 years
    3. 15 years
    4. 44 years
46. What is the inverse of the function f ( x ) = x − 4 ? f open x close equals , square root of x minus 4 end root . question mark
    6. f − 1 ( x ) = x 2 − 4 , x ≥ 0 f super negative 1 end super , open x close equals , x squared , minus 4 comma x greater than or equal to 0
    7. f − 1 ( x ) = x 2 − 4 , x ≥ 0 f super negative 1 end super , open x close equals , x squared , minus 4 comma x greater than or equal to 0
    8. f − 1 ( x ) = x + 4 f super negative 1 end super , open x close equals , square root of x plus 4 end root
    9. f − 1 ( x ) = x − 4 x − 4 f super negative 1 end super , open x close equals . fraction square root of x minus 4 end root , over x minus 4 end fraction

In Exercises 47 and 48, let f ( x ) = x 2 − 4 f open x close equals , x squared , minus 4  and g ( x ) = 1 x + 4 . g open x close equals . fraction 1 , over x plus 4 end fraction . .

47. What is ( g ∘ f ) ( x ) ? open g composition f close open x close question mark
    1. 1 x 2 fraction 1 , over x squared end fraction
    2. 1 x 2 − 8 x + 16 − 4 fraction 1 , over x squared , minus 8 x plus 16 end fraction . minus 4
    3. x 2 − 4 x + 4 fraction x squared , minus 4 , over x plus 4 end fraction
    4. x − 4 x minus , 4
48. What is ( f ∘ f ) ( 3 ) ? open f composition f close open 3 close question mark
    6. 1
    7. 5
    8. 21
    9. 77
49. What is the equation of the line shown below?

    

    1. y = − 4 5 x + 2 y equals negative , 4 fifths , x plus 2
    2. y = 5 4 x − 2 y equals , 5 fourths , x minus 2
    3. − 4 x + 5 y = 7 negative 4 x plus 5 y equals 7
    4. 4 x − 5 y = 15 4 x minus 5 y equals 15

Short Response

50. How much should you invest in an account that pays 6% annual interest compounded continuously if you want exactly $8000 after four years? Show your work.

Mixed Review

See Lesson 7-1.

Without graphing, determine whether the function represents exponential growth or exponential decay. Then find the y -intercept.

51. y = 23 ( 3.03 ) x y equals 23 . open , 3.03 , close to the x
52. f ( x ) = 3 ( 5 ) x f open x close equals 3 . open 5 close to the x
53. y = 2 ( 3 4 ) x y equals 2 . open , 3 fourths , close to the x
54. y = 5 ( 8 3 ) x y equals 5 . open , 8 thirds , close to the x

See Lesson 6-3.

Simplify.

55. 5 5 + 5 5 square root of 5 plus square root of 5
56. 4 3 − 2 4 3 cube root of 4 , , minus 2 , cube root of 4 ,
57. 75 + 125 square root of 75 plus , square root of 125
58. 32 4 + 128 4 the fourth , root of 32 , , plus , the fourth , root of 128 ,
59. 5 3 − 2 12 5 square root of 3 minus 2 square root of 12
60. 3 63 + 28 3 square root of 63 plus square root of 28

Get Ready! To prepare for Lesson 7-3, do Exercises 61–63.

See Lesson 6-7.

Find the inverse of each function. Is the inverse a function?

61. f ( x ) = 4 x − 1 f open x close equals 4 x minus 1
62. f ( x ) = x 7 f open x close equals , x to the seventh
63. f ( x ) = 5 x 3 + 1 f open x close equals , 5 x cubed , plus 1

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