C Challenge

Solve each equation.

47. 2 x = 64 2 to the x , equals 64
48. 3 x = 1 27 3 to the x , equals , 1 twenty seventh
49. 3 · 2 x = 24 3 middle dot , 2 to the x , equals 24
50. 5 · 2 x − 152 = 8 5 middle dot , 2 to the x , minus 152 equals 8

51. Suppose (0, 4) and (2, 36) are on the graph of an exponential function.

    1. Use (0, 4) in the general form of an exponential function, y = a · b x , y equals eh middle dot , b to the x , comma  to find the value of the constant a.
    2. Use your answer from part (a) and (2, 36) to find the value of the constant b.
    3. Write a rule for the function.
    4. Evaluate the function for x = − 2 x equals negative 2  and x = 4 . x equals 4 .

Standardized Test Prep

SAT/ACT

52. A population of 30 swans doubles every 10 yr. Which graph represents the population growth?

    1. 

    2. 

    3. 

    4. 

53. Which equation do you get when you solve y = 2 x − 12 y equals 2 x minus 12  for x?

    6. x = y − 6 x equals y minus 6
    7. x = y + 6 x equals y plus 6
    8. x = 0.5 y − 6 x equals 0.5 y minus 6
    9. x = 0.5 y + 6 x equals 0.5 y plus 6
54. Short Response 54. What are the solutions of the inequality 11 ≤ | x − 2 | + 4 ? 11 less than or equal to vertical line x minus 2 vertical line plus 4 question mark  Graph the solutions on a number line. Show your work.

Mixed Review

See Lesson 7-5.

Simplify each expression.

55. ( a 2 a 3 ) − 4 open . fraction eh squared , over eh cubed end fraction . close super negative 4 end super
56. ( m 4 n 2 ) − 7 open . fraction m to the fourth , over n squared end fraction . close super negative 7 end super
57. ( x 2 z z − 3 ) − 5 open . fraction x squared , z , over z super negative 3 end super end fraction . close super negative 5 end super
58. ( p q 0 p 4 ) 5 open . fraction p , q to the , over p to the fourth end fraction . close to the fifth

See Lesson 5-6.

Write an equation for the line that is parallel to the given line and passes through the given point.

59. y = 5 x + 1 ; ( 0 , 0 ) y equals 5 x plus 1 semicolon open 0 comma 0 close
60. y = 3 x − 2 ; ( 0 , 1 ) y equals 3 x minus 2 semicolon open 0 comma 1 close
61. y = 0.4 x + 5 ; ( 2 , − 3 ) y equals 0.4 x plus 5 semicolon open 2 comma negative 3 close

Get Ready! To prepare for Lesson 7-7, do Exercises 62–65.

See Lesson 2-10.

Tell whether each percent change is an increase or decrease. Then find the percent change. If necessary, round to the nearest percent.

62. original price: $25; sale price: $22
63. height last week: 15 cm; height this week: 18 cm
64. price this year: $999; price last year: $1450
65. birth weight: 220 lb; weight at 1 month: 300 lb

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