Intermediate Algebra (11th edition)

31.12.179 33. (a)0.6°C (b)0.3°C 35. (a)1.4°C (b)0.5°C

37. (a)5028 million tons (b)6512 million tons

(c)It is less than what the model provides (7099 million tons).

39. (a)$5000 (b)$2973 (c)$1768

(d) 41.6.67 yr after it was purchased

43. 4 45. 0

Section 10.3 (pages 592–595)

1. (a)B (b)E (c)D (d)F (e)A (f )C 3.


2. 
   
   
   
   7. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   13. 
       
       
       
       15. 
           
           
           
           17. 
               
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   21. 
       
       
       
       23. 
           
           
           
           25. 
               
           
           
           
           
       
       
       
       
   
   
   
   


5. (a)C (b)B (c)B (d)C 29. 31. 33.


6. 
   
   
   
   37. 
       
       
       
       39. 
           
           
           
           41. 
               
               
               
               43. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


7. 
   
   
   
   47. 
       
       
       
       49. 
           
           
           
           51. 
               
           
           
           
           
       
       
       
       
   
   
   
   

53.Every power of 1 is equal to 1, and thus it cannot be used as a base.

55. ; 57. 8 59. 24 61. (a)4385 billion ft^3

(b)5555 billion ft^3 (c)6140 billion ft^3 63. (a)130 thousand units
(b)190 thousand units (c)

65.about 4 times as powerful

t

S(t)

0

50

100

150

200

250

10 20 30 40

S(t) = 100 + 30 log 3 (2t + 1)

1 0, q 21 - q, q 2

x

y

0 4 12 20

2

–3 y = log

y = log1/31/3xx

x

y

0 4 12 20

2

–3 y = log

y = log 33 x

E^32 F^5306

516 5 x|x 7 0, xZ (^16556) E 35 F 546
E^13 F^5816 E^15 F
A^14 B 5 -^1 = 5 -^1
1/2
60 = 1 9 1/2= 3 =^12
log 8 41 =-^23 log 5 1 = 0 43 = 64 10 -^4 =10,000^1
log1/2 8 =- 3 log 10 0.001=- 3 log 625 5 = 41
log 4 1024 = 5
t
V(t)
0
1000
2000
3000
4000
5000
2 4 6 8 10 12
Years
Dollars
V(t) = 5000(2)–0.15t
Connections ( page 601) 1.
A calculator gives
2.Answers will vary.

Section 10.4 (pages 602–603)

1. 
   
   
   
   3. 4 5. 9 7.
   
   
   
   


2. 
   
   
   
   11. 
       
       
       
       13. 
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   17. 19.In the notation , the parentheses do not indicate multipli-
       cation. They indicate that is the result of raising ato some power.
   
   
   
   


4. 
   
   
   
   23. 
       
       
       
       25. 
           
           
           
           27. 
               
           
           
           
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   31. 33.1.2552 35. 0.6532
   
   
   
   

37.1.5562 39.0.2386 41.0.4771 43.4.7710 45.false

47.true 49.true 51.false 53.The exponent of a quotient is the

difference between the exponent of the numerator and the exponent of

the denominator. 55.No number allowed as a logarithmic base can be

raised to a power with a result of 0. 57.

59. 
    
    
    
    61. 
        
    
    
    
    

Section 10.5 (pages 609–612)

1.C 3.C 5.31.6 7.1.6335 9.2.5164 11.

13.9.6776 15.2.0592 17. 19.5.9613 21.4.1506

23.2.3026 25. (a)2.552424846 (b)1.552424846

(c)0.552424846 (d)The whole number parts will vary, but the decimal

parts are the same. 27.poor fen 29.bog 31.rich fen 33.11.6

35.4.3 37. 39. 41. (a)107 dB

(b)100 dB (c)98 dB 43. (a)800 yr (b)5200 yr (c)11,500 yr

45. (a)77% (b) 1989 47. (a)$54 per ton (b)If , then
    , so Twould be negative. If , then
    , but the domain of ln xis 49.2.2619
    51.0.6826 53.0.3155 55.0.8736 57.2.4849 59.Answers will
    vary. Suppose the name is Jeffery Cole, with and.
    (a) is the exponent to which 7 must be raised to obtain 4.
    (b)0.7124143742 (c) 4 61.6446 billion 63.


46. 
    
    
    
    67. 
        
        
        
        69. Connections ( page 619) 2
        
        
        
        
    
    
    
    

–2

• 250

{5} {-3} log 1 x+ 221 x+ 32 , or log 1 x^2 + 5 x+ 62

ft^3 E-^35 F

log 7 4

m= 7 n= 4

ln 11 - p 2 =ln 0 1 0, q 2.

ln 11 - p 2 =ln 1= 0 p= 1

p= 0

4.0* 10 -^8 4.0* 10 -^6

• 2.8896
  
  
  • 1.4868
  
  
  
  

log 10 0.01=- 2 100 = 1

log 10 10,000= 4

logp -

x^3 y1/2

z3/2a^3

log 10 1 x^2 - 92

loga

125

81

loga

rt^3

s

loga

m

n

logb xy

x+y

loga 1 x+y 2

1

3 log 2 x+

1

5 log 2 y-2 log 2 r

1

2 log 3 x+

1

2 log 3 y-

1

2 log 3 5

1

log 5 8 - log 5 3 2 log 4 6 3 log 3 4 - 2 log 3 x-log 3 y

log 10 7 +log 10 8 log 7 4 +log 7 5

1 458.3 21 294.6 2 =135,015.18.

10 5.130382600L135,015.18

L5.130382600

+log 10 294.6L2.469232743

9. log 10 458.3L2.661149857

x

y

0

yy = 4 = 4––xx

–1

67. 
    
    
    
    69. 
        
    
    
    
    


68. 49 73. 712

10

–10

–10 10

g(x)

13.rises; falls

15. 
    
    
    
    17. 
        
    
    
    
    


16. 
    
    
    
    21. 
        
    
    
    
    


17. 
    
    
    
    25. 27.639.545 29.0.066
    
    
    
    

5 - 16 5 - 36

576 5 - 36

526 E^32 F

11.

x

y

–2 02

2

4

6

8

yy = 2 = 2^22 x x – 2– 2

10

–10

–10 10

g(x)

Answers to Selected Exercises A-25