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8.1 Products and Powers

1. x8

2. y5

3. x7y5

4. m5n7p4

5. 12w7

6. –35z17

7. a12

8. b14

9. c13

10. d27

11. 4b4c2d10

12. –a12

13. –10a2b3

14. 36x6

15. –12a4b2c2

16. –2x5y8z3

17. 500x11

18. 250x24y11

19. –45x9y3z22

20. –9

2x

12

y23

Section 8.1

22. 64x33y9

23. 5b2c2 – bc2

24. –9g5h7

25. 7x5y4 – 6x4y5

26. 5w3z2 – w2z3

27. 6x5y2

28. 36a7

29. 1

6h

6

30. 27a9b3

31. xn + 3

32. 25

33. a2x + 2

34. y5z + 3

35. 3x2y2 – 2xy3

36. 10a5b + 14a3b5

37. –4r4s3 + r2s5

38. –5

2m

8

n6 + 10

3 m

6

n9

39. (abc)3 = (abc)(abc)(abc)

40.

10243 230 1 billion 109

10244 240 1 trillion 1012

10245 250 1 quadrillion 1015

10246 260 1 quintillion 1018

10247 270 1 sextillion 1021

41. the product of x factors of b

42. 2 2 2 8

3 × × =3 3 27

43. 1 1

–2(–2)(–2)(–2) = 16

44. –3(3)(3)(3) = –81

45. –5 5

4 4

⎛ ⎞ ⎜ ⎟

⎝ ⎠ = –

25 16

46. the number 0

47. The coefficient is 1.

48. The exponent is 1.

49. Its slope is undefined.

8.2 Quotients

1. 9x5

2.

4

3 2

y

3. –

5

3 4

ab

4. –

4

6

r s

5. z2

6. 1₅

x

7. 2₃

x

8. y

x

9. x

10. z5

11. 1

12. – 1₃

jk

13.

6 15

x y

14.

3 6

15. 3 3 x y 16. 3 3 y x

17. 8x5y–9

18. –3a–1b8

19. 1

5b

–9

c–5

20. 4x5y–5

21. –5a2b–5c4

22. a–4b–4c–4

23. – 3 6 7 x z 24. 4 6

19x y

z 25. – 6 5 11 a c b 26. 4 4 2 3 x y

27. 1₃

2a

28.

2

ay bc

29. ₄1 ₄

x y

30. ₄1 ₉

Section 8.2 31. – 2 3 3 a bc 32. 9 4 9 y x

33. 3a–3b or 3b₃

a

34. ₂

2

r s

35. 6x

36. 2

3

37. a2

38. y2a

39. x2a – b

40. b3x + 5

41.

2 4

x

y – 1

42. 1₂

c +

3 3 5

a b c

43. 1₂

rs – 3

44. ₄3 ₂

m n + 4m

3 45. 3 a b ⎛ ⎞ ⎜ ⎟

⎝ ⎠ = (ab–1)3 = a3b–3 =

3 3

a b

47. 0.85 sec

48. 0.25 sec

49. D = {–2, 4, 8, 9};

R = {4, 8, 9}; yes

50. D = {–19.2, 1.7, 6.4};

R = {–18, –3.5, 18.2}; yes

51. rate; time

52. inverse

53. t(r) = 300

r

54. y = 1

2x – 3

55. y = –2x + 6

56. y = 2x + 8

57. x = –3

58. y = 2

8.3 Scientific Notation

1. 3.9 × ₁₀8

2. 2.73 × ₁₀5

3. 5.2 × ₁₀–5

4. 3.2 × ₁₀–3

5. 1.36 × ₁₀8

6. 1.067 × ₁₀–5

7. 2.356 × ₁₀–2

8. 1.358 × ₁₀10

9. 254,000,000

10. 34,000,000

11. 0.000153

12. 0.00000289

13. 6 × ₁₀7

14. 2.4 × ₁₀15

15. 8.1 × ₁₀21

16. 3 × ₁₀5

17. 5 × ₁₀6

18. 1.25 × ₁₀–7

19. 9.5 × ₁₀3

21. 2.77 × ₁₀9

22. 1.247 × ₁₀8

23. 3.01 × ₁₀3

24. 2.5 × ₁₀–6

25. 5.625 × ₁₀–29

26. 5.54 × ₁₀15

27. 2.73 × ₁₀7

28. 8 × ₁₀6

29. capillary: 8 × ₁₀–6 _m;

aorta: 2.5 × ₁₀–2 _m

30. 7.94 × ₁₀8 _mi

31. 5 × ₁₀2 _sec

32. 2 × ₁₀2 _cells

33. 2.25 × ₁₀2 _km

34a. 1.2 × ₁₀–9 _sec

34b. 1.2 × ₁₀0 _or

1.2 nanoseconds

35. 7 × ₁₀5

36. 1.5 × ₁₀11

37. 1

38. 2 × ₁₀6

39. 6 × ₁₀5

Section 8.3

y

x

(3, 4)

41. 314 × ₁₀3 _{= 314 thousand}

42. 189 × ₁₀9_{; 189 billion}

43. 53.85 × ₁₀–6_;

53.85 millionths

44. 100 × ₁₀–6_{; 100 millionths}

45. 1, 000, 000, 000, 000, 000, 000, 000

46. 1 × ₁₀21

47. 8 × ₁₀32 _bytes

48. ≈ _1.17 × ₁₀23 _bytes;

117 zettabytes

49. Answers will vary.

50. 1

7

51. –3

2

52. 5x + 2y = –10

53. 4x – y = –10

y

x

(2, ₂2)

55.

56. (0, 2)

57. (2, 3)

58. (0, 2)

8.4 Translating Power Functions

1. 5 units up

2. 4 units right

3. 7 units left

4. 12 units down

5. 5 units right, 6 units up

6. 1 unit left, 9 units down

7. h units right, k units up

8. h units left, k units down

9. (3, 1)

10. (15, –9)

11. (–8, 6)

12. (–3, –1)

13. (0, 19)

14. (–12, 0)

15. (7, 0)

16. (0, –5)

17. (h, –k)

19. (0, 3)

x y

20. (1, 0)

y

x

21. (–2, 0)

x y

22. (0, –2)

Section 8.4

23. (4, 1) y

x

24. (–1, –5) y

x

25. f(x) = (x – 10)2

26. f(x) = x2 – 5

27. f(x) = (x + 3)2 – 12

28. f(x) = (x – 7)2 + 2

29. f(x) = (x – 2)2 + 1

30. f(x) = (x + 6)2 – 3

31. y = x2 + 2

32. y = (x + 3)2

33. y = (x – 2)2 –2

y

x

y

x

35. 36.

x 3x2

–2 –24

–1 –3

0 0

1 3

2 24

x 1

2x

2

–2 2

–1 1

2

0 0

1 1

2

Section 8.4 y

x

37.

38. It gets “steeper.”

39. It gets “wider.”

40. It turns upside down.

41. 2 units down

42. 5 units right

43. 12 units left, 3 units up

44. 15 units right, 1 unit down

45. e

46. b

47. c

48. (8, 1)

49. (–3, –2)

50. (10, 9)

x –x2

–2 –4

–1 –1

0 0

1 –1

y

x

8.5 Exponential Functions

1. 1

32

2. 1

81

3. 192

4. –3

8

5.

x y

–2 1

9

–1 1

3

0 1

1 3

Section 8.5

y

x

6. _{x y}

–2 9

–1 3

0 1

1 1

3

2 1

y

x 7.

x y

–3 27

8

–2 9

4

–1 3

2

0 1

1 2

3

2 4

9

Section 8.5

y

x

y

x

2

22 2

4 6 8 10 12 14 16 18

8. 9.

x y

–3 8

27

–2 4

9

–1 2

3

0 1

1 3

2

2 9

4

3 27

8

x y

–2 2

9

–1 2

3

0 2

1 6

y

x

5

22 2

10 15 20

10.

x y

–2 18

–1 6

0 2

1 2

3

2 2

Section 8.5 y x 2 4 6 8 10

22 2

y

x

2

22 2

4 6 8 10 12 14 16 18

11. 12.

x y

–3 81

8

–2 27

4

–1 9

2

0 3

1 2

2 4

3

3 8

9

x y

–3 32

27

–2 16

9

–1 8

3

0 4

1 6

2 9

3 27

13. e

14. d

15. As x increases, y decreases.

16. As x increases, y increases.

17. y = 1.25x; 156%

18. y = 0.6x; = 22%

19. y = 0.75x; 32%

20. y = 1.25x; 195%

21a. $1020.00

21b. $1040.40

21c. $1218.99

21d. $1640.61

21e. $2691.59

22a. 500 bacteria

22b. 4000 bacteria

22c. 2.048 × 106 bacteria

Section 8.5

y

x

y

x

23. 24.

x y

–2 _–1

9

–1 _–1

3

0 –1

1 –3

2 –9

x y

–2 –9

–1 –3

0 –1

1 _–1

3

2 _–1

y

x

y

x

25. 26.

x y

–2 9

–1 3

0 1

1 1

3

2 1

9

x y

–2 1

9

–1 1

3

0 1

1 3

Section 8.5

y

x

27. Answers will vary.

Sample response: y = bx and

y = – bx are mirror images

(reflections) of each other

across the x-axis.

28. Answers will vary. Sample

response: y = bx and y = b–x

are mirror images

(reflections) of each other

across the y-axis.

29.

x y

–2 13

4

–1 7

2

0 4

1 5

30. y 5 bx 1 c is a vertical

translation (by c units) of

y 5 bx. 31. a 32. c 33. d 34. b 35. 2 36. $10,737,418.24

37. y = a; The graph is a

horizontal line.

38. No; if 0 < b < 1, then the

function decreases.

39. 1

2 x − ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ = 2 1 x ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ = 2 1 x

x =

2 1

x

= 2x

40. 1 × 109

41. 1 × 10–6

42. 1.86 × 105 miles

43. 6 × 1012 miles

44. 6 × 1017 miles

45. 1.32 × 1019 miles

46.

y

Section 8.5 47.

48. rs3

49. ₅3 ₃

m n

50. ₃c ₂

a b

51. xz₅

y

52. 42 mi

53. boat: 25 mi/hr; current: 5 mi/hr

54. 222mL of concentrated acid and 788 mL of water

55. $7500 at 6% and $2500 at 2%

8.6 Exponential Growth and Decay

1. 35; 5%; 1.05; growth

2. 16; –20% 0.8; decay

3. 1; –30%; 7

10; decay

4. 10,000; 10% 1.1; growth

5. f(t) = 10(2.5)t; growth

6. f(t) = 0.5(0.7)t; growth

7. f(t) = 81 3

2 t

⎛ ⎞ ⎜ ⎟

⎝ ⎠ or

f(t) = 81(1.5)t; growth

8. f(t) = 125(0.2)t or

f(t) = 125 1

5 t

⎛ ⎞ ⎜ ⎟

⎝ ⎠ ; decay

9. f(t) = 75(0.5)t or

f(t) = 75 1

2 t

⎛ ⎞ ⎜ ⎟

⎝ ⎠ ; decay

10. f(t) = 60,000 3

2 t

⎛ ⎞ ⎜ ⎟

⎝ ⎠ or

f(t) = 60,000(1.5)t; growth

11. y = 800,000(0.9)x

12. y = 200(1.03)x

Section 8.6

14. y = 4000 3

4

x

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

15. 10 periods; 6%

16. 20 periods; 3%

17. 40 periods; 1.5%

18. 120 periods; 0.5%

19. 3650 periods; ≈0.016%

20. 5000(1.04)10

21. 5000(1.02)20

22. 2000(1.0075)80

23. 37,855

(

)

24. 500(1.00016)3650

25. f(q) = 10,000(1.015)q;

f(48) = $20,434.78

26. f(q) = 4500(1.011)q;

f(32) = $6386.30

27. f(h) = 2000(1.03)h;

f(40) = $6524.08

28. f(m) = 2000(1.005)m;

f(240) = $6620.41

29. f(n) = 5000(1.045)n;

f(6.5) = $6656.19

30a. f(x) = 25,000(1.02)x

30b. 30,475; 37,149; 45,284;

0 1 2 3 4 5 0 2 1 3 4 5 Bouncing Ball

Number of Bounces

Height (m)

30c.

31a. f(x) = 500(0.9)x

31b. 328 mg

31c.

32a. f(x) = 10 2

5

x

⎛ ⎞ ⎜ ⎟

⎝ ⎠ or

f(x) = 10(0.4)x

32b. 0.1024 m

32c.

33a. f(n) = 0.01(2)n

33b. 10.24 cm

1990 2000 2010 2020 2030 2040 2050 10,000 0 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000

Population of Greenwood

Section 8.6

1

0 2 3 4 5 6 7 8 9 10 11 0

1 2 3 4 5 6 7 8 9 10 11

Paper Folding

Number of Folds

Thickness (cm)

33c.

34a. f(q) = 500(2)p

34b. 32,000 bacteria

34c. 2.4 × 1024 bacteria

35a. f(m) = 2

( )

m

35b. f(n) = 2(2)4n or

f(n) = 2(16)n

35c. 8192 squirrels

36. b > 1

37. 0 < b < 1

38. b ≤ 0; b = 1

39a. $153

39b. $79

39c. $54

39d. $285 or $286

40. 2.325 × 108 = 232,500,000

41. 2.001 × 109 = 2,001,000,000 people

42. 1.20 × 102 = 120 emails

43. 1.25 × 103 = 1250 messages

per second

44. Answers will vary. Typical answers might include

sharing your faith through social networking sites, providing access to

Christian music and

messages through websites, or sharing your faith

through blogs.

45. no

46. yes

47. y < –1

3x + 3 and y ≤ x + 4

48. x ≥ 2, y ≥ 1, and y < –x + 7

49. y = –2x + 3; consistent

dependent

50. (2, –1); consistent independent

51. ∅; inconsistent

52. –9

4xy

Section 8.6

53.

8 11

9x y

Chapter 8 Review

1. –18m3n12

2. 27g6h3

3. 9a3b2

4. 2w5z2

5. 4m2np4

6. xy7

7. x3

8. y2a

9. 2x

10. –8j3k4

11. –3m–4r5s–6

12. 2a–2b5c

13. 3 3 2

4 x y

− − − 14. 4 b a 15. 3 6 15 – y x z 16. 8 3 yz x 17. 10 6 4 b a

Chapter 8 Review

x y

19. 3.19 × 10–4

20. 32,000

21. 3 × 105

22. 3 × 102

23. 1.25 × 1014

24. 8.3 × 103

25. 5.4 × 10–2

26. 1 × 10–10 m

27. 1.08 × 109 km

28. (1, 0)

29. (0, 7)

30. (–3, 5)

31. (2, –4)

y

x

y

x

y

x

22 2

4 8 12 16

33. 3 units right, 2 units up

34. f(x) = (x – 5)2 + 3

35. y = (x + 1)3 – 2

36. y = 3x

37. –2

9

38. 12.5

39.

Chapter 8 Review

41. (0, 1)

42. 0 < b < 1

43. 1; 50%; 1.5; growth

44. 10,000; –66.6%; 1

3; decay

45. y = 0.8x; 51.2%

46. y = 1.2x; 144%

47. f(x) = 50,000(1.05)x;

$81,445

48. f(d) = 125 2

5

d

⎛ ⎞ ⎜ ⎟

⎝ ⎠ or

f(d) = 125(0.4)d; 32

25 cm

2

or

1.28 cm2

49. 40 periods; 0.75%; $6741.74

50. 120 periods; 0.25%; $6746.77

51a. 200%; 3

51b. f(d) = 500(3)d

U-237 Sample

Number of Weeks

Amount of Sample (g)

0 1 2 3 4 5

0 4 2 6 8 10 12 14 16 18

52a. f(w) = 16 1

2

w

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

52b. 0.5 or 1

2g

Sequences—Infinite Geometric Sums

1. yes; r = 1

5

2. no; r = 2, so the sequence diverges

3. no; arithmetic sequences diverges

4. yes; r = –1

2

5. 1

6. 8

3

7. 3

2

8. impossible (r = 3)

9. 7

9

10. 4