Intermediate Algebra (11th edition)

27. 
    
    
    
    28. 
        
    
    
    
    


28. 
    
    
    
    30. 31.1.4609 32.
    
    
    
    

33.3.3638 34. 35.0.9251 36.1.7925 37.6.4

38.8.4 39. 40.Magnitude 1 is about 6.3 times as

intense as magnitude 3. 41. (a)18 yr (b)12 yr (c)7 yr

(d)6 yr (e)Each comparison shows approximately the same number.

For example, in part (a) the doubling time is 18 yr (rounded) and.

Thus, the formula (called the rule of 72) is an excellent

approximation of the doubling time formula. 42.

43. 
    
    
    
    44. 
        
        
        
        45. 
            
            
            
            46. 
                
            
            
            
            
        
        
        
        
    
    
    
    


44. 
    
    
    
    48. 
        
        
        
        49. 
            
            
            
            50. 51.When the power rule
                was applied in the second step, the domain was changed from
                to. The valid solution was “lost.” The solution set is
                52.$24,403.80 53.$11,190.72 54.Plan A is better, since
                it would pay $2.92 more. 55.about 13.9 days 56. (a)about $4267
                (b)about 11% 57.about 67% 58.D 59. 7 60. 36 61. 4
                62.e 63. 64.5.4 65. 66. 67. 68.
            
            
            
            
        
        
        
        
    
    
    
    


45. 
    
    
    
    70. 
        
        
        
        71. 
            
            
            
            72. 
                
                
                
                73. 
                    
                    
                    
                    74. (a)
                        (b)The x-value of the x-intercept is 0.375, the decimal equivalent of.
                        75.about 32.28% 76. (a)0.325 (c)0.673
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    

Chapter 10 Test (pages 630–632)

[10.1]1. (a)not one-to-one (b)one-to-one 2.

3. [10.2]4. [10.3]5.

[10.1–10.3]6.Once the graph of is sketched, interchange the

x-and y-values of its ordered pairs. The resulting points will be on the

graph of since ƒand gare inverses. [10.2]7.

8. [10.5]9. (a)55.8 million (b)80.8 million
   [10.3]10. 11. 12. 13.


9. 15.5; 2; fifth; 32 [10.4]16.


10. 
    
    
    
    18. 
        
        
        
        19. 
            
        
        
        
        
    
    
    
    

[10.5]20. (a)1.3636 (b) 21. (a) (b)

(c)2.6801 [10.6]22. 23. 24.$12,507.51

25. (a)$19,260.38 (b)approximately 13.9 yr

Chapters 1–10 Cumulative Review Exercises

(pages 632–633)

[1.1]1. 0, 6, 2. , 0, 0.6, 6,

3. , [1.2, 1.3]4. 16 5. [2.1]6.
   [2.5]7. 3 1, q 2 [2.7]8. 5 - 2, 7 6 9. 1 - q, - 32 ́ 1 2, q 2
   
   
   • 22 211 - 39 E- 32 F
   
   
   
   

30

• -2, 3 1 or 10 2
  9
  4

30

• 2, 3 1 or 10 2

5 3.966 6 536

ln 19

ln 3

log 19

log 3

• 0.1985

logb

r1/4s^2

t2/3

logb

s^3

t

1

2 log 5 x-log 5 y-log 5 z

526 2 log 3 x+log 3 y

log 4 0.0625=- 2 72 = (^495326) E^12 F
E-^133 F
g 1 x 2 =log 6 x 5 - 46
ƒ 1 x 2 = 6 x
x
y
0
–3
2
2468
g(x) = log 6 x
x
y
2
2
4
6
8
–2
ff((xx) = 6) = 6xx
0
x
y
0
4
–2
ƒ -^11 x 2 =x^3 - 7
3
8
536 506 E^18 F E^113 F 5 - 2, - 16 E^38 F

• 
  

  (^55726536) E 91 F E^43 F
  5  106.
  5 x|x 706 - 10
  5 x|xZ 06
  (^526) E^38 F 546 516
  5 4.907 6 5 18.310 6 E 91 F E- 6 + 2325 F
  5 2.042 6
  t=
  72
  100 r
  72
  4 =^18
  2.5* 10 -^5

  
  


• 
  

  1.3587

  
  

log 3 a -0.5901

x+ 7

4 x+ 6

logb b

3 x

y^2

1

log 2 3 +log 2 x+2 log 2 y 2 log 4 x+2 log 4 w-log 4 z

A-26 Answers to Selected Exercises

Section 10.6 (pages 619–622)

1. 
   
   
   
   3. 
      
      
      
      5. 
         
         
         
         7. 
            
            
            
            9. 
               
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   13. 
       
       
       
       15. 
           
           
           
           17. 
               
           
           
           
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   21. 
       
       
       
       23. 25.Natural
           logarithms are a better choice because eis the base. 27.
       
       
       
       
   
   
   
   


4. 
   
   
   
   31. 33.2 cannot be a solution because
   
   
   
   

, and is not in the domain of log x.

35. 
    
    
    
    37. 
        
        
        
        39. 
            
            
            
            41. 
                
                
                
                43. 
                    
                    
                    
                    45. 
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


36. (a)$2539.47 (b)10.2 yr 49. (a)$4934.71 (b)19.8 yr


37. (a)$11,260.96 (b)$11,416.64 (c)$11,497.99 (d)$11,580.90
    (e)$11,581.83 53.$137.41 55. (a)15.9 million tons

(b)30.7 million tons (c)59.2 million tons (d)93.7 million tons
57.$143,598 million 59. (a)1.62 g (b)1.18 g (c)0.69 g

(d)2.00 g 61. (a)179.73 g (b)21.66 yr 63. 2012 65.It means
that after 250 yr, approximately 2.9 g of the original sample remain.

67. 
    
    
    
    69. 
        
    
    
    
    

Chapter 10 Review Exercises (pages 626–630)

1.not one-to-one 2.one-to-one 3.

or 4. 5.not one-to-one

6.This function is not one-to-one because two sodas in the list have
41 mg of caffeine.

ƒ -^11 x 2 =x

(^3) + 4
6
ƒ -^11 x 2 =-^1
3
x+^7
3
ƒ -^11 x 2 =
x- 7

• 3
  ,

x

y

0 1

4

ff((xx) = () = (x x + 1)+ 1)^22

x –3

y

01

8

2 ff((xx) = 2) = 2xx^22

E^13 F 526 0 586 E 34 F 586

log 12 - 32 =log 1 - 12 - 1

E^332 F E-^1 +^2349 F

E^23 F

5 5.879 6 5 - p 6 , or 5 - 3.142 6 516

5 - 6.067 6 5 261.291 6 5 - 10.718 6 536

5 0.827 6 5 0.833 6 5 1.201 6 5 2.269 6 5 15.967 6

23. 
    
    
    
    24. is the exponent to which
        bmust be raised to obtain a. 25.a
    
    
    
    


24. (a)$300,000 (b)

x

S(x)

02468

(^100) S(x) = 100 log 2 (x + 2)
200
300
400
Weeks
Sales (in thousands
of dollars)
Eb|b 7 0, bZ 1 F logb a

7. 
   
   
   
   8. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   

x

y

2

2

4

6

8

–2

ff((xx) = 3) = 3 xx

0

x

y

0

2

2

f –1

f

x

y

f–1

f

0

3

3

10. 
    
    
    
    11. 
        
        
        
        12. 
            
            
            
            13. 
                
            
            
            
            
        
        
        
        
    
    
    
    

14.E^37 F

E^12 F^546

x

y

2

4

8

12

16

–2

yy = 2 = 2^22 xx + 3+ 3

x 0

y

2

2

4

6

8

–2

ff((xx) = ) = xx

0

1

( 3 )

15. (a)29.4 million tons (b)18.2 million tons (c)14.4 million tons


16. 
    
    
    
    17. 
        
        
        
        18. 
            
            
            
            19. 
                
            
            
            
            
        
        
        
        
    
    
    18. 
        
        
        
        21. 
            
        
        
        
        
    
    
    19. 546
    
    
    
    

576 586

526 E^32 F

x

y

0

–3

(^241220)
g(x) = log 1 / 3 x
x
y
–2^0
2
4
2468
g(x) = log 3 x