43,49,55,61 Problems 73-86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.. (a) Graph f(x) = 3* and g(x) = 10 on the same Cartesian n Source: U.S. Census Bureaub) Shade the region bounded by the y-axis, f(x) = 3*,(3) Solve f(x) = g(x) and label the point of intersectionb) Shade the region bounded by the y-axis, f(x) = 2*,1L(2) Graph f(x) = 2 and g (x) = 12 on the same Cartesianand g(x) = 12 on the graph drawn in part (a).l) Solve f(x) = g(x) and label the point of intersectionpress irrational solutions in exact form.46. 5* = 25Problems 43)47. 2' = 1050. 2* = 1.548. 3 = 1451. 5(2) = 854. 2r+1 = 5!-2r52. 0.3 (40.2x) = 0.2AS= 1.2()55.= 71-x58. 0.31+x = 1.72r-1= 5*1A12 (0.5)-*4l. 2 + 2-12 = 0S 16 + 4** - 3 =03-4" + 4.2" + 8 = 056.62. 32x + 3* - 2 = 066. 9* - 3*+1 + 1 = 059. 7-x = et63. 32* + 3*+1 - 4 = 0you60. e*+3 =the64. 22 + 2*+2 – 12 = 0mal70. 2.49* + 11 7* + 5 = 067. 25* - 8.5* = -1668. 36* - 6.6* = -971. 4 - 10.4* = 372. 3 - 14.3* = 5(e)sl v76. e2r = x + 280. In (2x) = -x + 284. e - In x = 474. log2(x - 1) – log,(x + 2) = 277. e = x?78. e = x81. In x = x – 1In.r= -r82. In x = -x?85. e* = In xa+ Inx = 486. e* = -In xAlications and Extensions93. (a) Graph f(x) = 2*+1 and g(x) = 2*+2 on the sameSolve f(x) = 3. What point is on the graph of f?(e Solve g(x) = 4. What point is on the graph of g?Solve f(x) = g(x). Do the graphs of f and g intersect?Cartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 2**1,and g(x) = 2x+2 on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersectionon the graph drawn in part (a).(c)If so, where?(d) Solve (f + g) (x) = 7.(e) Solve (f – 8) (x) = 2.& (x) = log3 (x + 5) and g (x) = log3 (x - 1).(2) Solve f(x) = 2. What point is on the graph of f?6) Solve g (x) = 3. What point is on the graph of g?(6) Solve f(x) = g(x). Do the graphs of f and g intersect?If so, where?(d) Solve (f + g) (x) = 3.(e) Solve (f – g) (x) = 2.8. (a) If f(x) = 3**1 and g(x) = 2**2, graph f and g on thesame Cartesian plane.(b) Find the point(s) of intersection of the g:ss of fand gby solving f(x) = g(x). Round areters to threedecimal places. Label any intersection points on thegraph drawn in part (a).(c) Based on the graph, solve f(x) > g(x}.* (0) If f(x) = 5*-1 and g(x) = 2*+1 graph f and g on thesame Cartesian plane.O Find the point(s) of intersection of the graphs of f and gby solving f(x) = g(x). Label any intersection pointson the graph drawn in part (a).O Based on the graph, solve f(x) > g(x). 3 dep94. (a) Graph f(x) = 3*+1 and g(x) = 3*-2 on the sameCartesian plane.(b) Shade the region bounded by the y-axis, f(x)and g (x) = 3*-2 on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersectionon the graph drawn in part (a).3*+1,a95. (a) Graph f(x) = 2* – 4.(b) Find the zero of f.(c) Based on the graph, solve f(x) < 0.96. (a) Graph g(x) = 3* – 9.(b) Find the zero of g.(c) Based on the graph, solve g(x) > 0.97. A Population Model The resident population of the UnitedStates in 2018 was 327 million people and was growing ata rate of 0.7% per year. Assuming that this growth ratecontinues, the model P(t) = 327 (1.007)the population P (in millions of people) in year t.(a) According to this model, when will the population of theUnited States be 415 million people?1-2018representsa bat MIs intere (b) According to this model, when will the population of theUnited States be 470 million people?plane.98. A Population Model The population of the world in 2018was 7.63 billion people and was growing at a rateof 1.1% per year. Assuming that this growth rate continues,the model P(t) = 7.63(1.011)-2018 represents thepopulation P (in billions of people) in year t.(a) According to this model, when will the population of theworld be 9 billion people?(b) According to this model, when will the population of theworld be 12.5 billion people?and g (x) = 10 on the graph drawn in part (a).on the graph drawn in part (a).plane.i the graph drawn in part (a).Source: U.S. Census Bureau 3. Approximate the solution(s) to x = x²utility. (pp. B6-B8)5 using a grupi U LUgrapilng utim )Skill BuildingIn Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.7. log2 (5x) = 46. log (x + 6) = 1log, 155. log4 x = 2dt oto 10. log5(2x + 3) = log, 38. log3 (3x – 1) = 29. log4 (x + 4)no w d13. logs 2x – 1| = log5 1311. log4|x| = 312. log2|x7 = 416. -2 log4 x = log4 914. log9|3x + 4| = log9|5x – 12|15. - log7 x = 3 log7 219. 2 log6(x - 5) + log, 9 = 217. 3 log2 x = -log2 2718. 2 logs x = 3 log5 422. log x + log (x – 21) = 220. 2 log3 (x + 4) – log3 9 = 221. log x + log (x + 15) = 225. log2 (x + 7) + log2(x + 8) = 1|28. logs (x + 3) = 1 – log3(x – 1)31. log9 (x + 8) + log,(x + 7) =234. log4 (x – 9) – log,(x + 3) = 336. log, x + log, (x – 2) = loga(x + 4)38. log3 x - 2 log3 5 = log3(x + 1) – 2 log; 1023. log (7x + 6) = 1 + log (x – 1)24. log (2x) – log (x – 3) = 126. logo(x + 4) + log6(x + 3) = 127. logs (x + 6) = 1 – logs(x + 4)-29. In x + In (x + 2) = 430. In (x + 1) – In x = 232. log2 (x + 1) + log2(x + 7) = 333. log1/3 (x + x) – log1/3 (x² – x) = -135. log. (x – 1) – log.(x + 6) = loga(x - 2) – loga(x + 3)37. 2 log5 (x – 3) – log5 8 = log5 239. 2 log, (x + 2) = 3 log, 2 + log, 440. 3(log7 x – log, 2) = 2 log, 441. 2 log13 (x + 2) = log13(4x + 7)deups latnonogx43. (log3 x)2 – 3log3x = 10i booubo42. log (x – 1) =log 244. In x - 3V In x + 2 = 0Bob mo ghbiozerc pe aojogo

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Description: 43,49,55,61 Problems 73-86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.. (a) Graph f(x) = 3* and g(x) = 10 on the same Cartesian n Source: U.S. Census Bureaub) Shade the region bounded by the y-ax

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Algebra for College Students

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ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter8: Functions

Section8.3: Quadratic Functions

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43,49,55,61

Problems 73-86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.
. (a) Graph f(x) = 3* and g(x) = 10 on the same Cartesian n Source: U.S. Census Bureau
b) Shade the region bounded by the y-axis, f(x) = 3*,
(3) Solve f(x) = g(x) and label the point of intersection
b) Shade the region bounded by the y-axis, f(x) = 2*,
1L(2) Graph f(x) = 2 and g (x) = 12 on the same Cartesian
and g(x) = 12 on the graph drawn in part (a).
l) Solve f(x) = g(x) and label the point of intersection
press irrational solutions in exact form.
46. 5* = 25
Problems 43)
47. 2' = 10
50. 2* = 1.5
48. 3 = 14
51. 5(2) = 8
54. 2r+1 = 5!-2r
52. 0.3 (40.2x) = 0.2
AS= 1.2
()
55.
= 71-x
58. 0.31+x = 1.72r-1
= 5*
1A12 (0.5)-*
4l. 2 + 2-12 = 0
S 16 + 4** - 3 =0
3-4" + 4.2" + 8 = 0
56.
62. 32x + 3* - 2 = 0
66. 9* - 3*+1 + 1 = 0
59. 7-x = et
63. 32* + 3*+1 - 4 = 0
you
60. e*+3 =
the
64. 22 + 2*+2 – 12 = 0
mal
70. 2.49* + 11 7* + 5 = 0
67. 25* - 8.5* = -16
68. 36* - 6.6* = -9
71. 4 - 10.4* = 3
72. 3 - 14.3* = 5
(e)
sl v
76. e2r = x + 2
80. In (2x) = -x + 2
84. e - In x = 4
74. log2(x - 1) – log,(x + 2) = 2
77. e = x?
78. e = x
81. In x = x – 1
In.r= -r
82. In x = -x?
85. e* = In x
a+ Inx = 4
86. e* = -In x
Alications and Extensions
93. (a) Graph f(x) = 2*+1 and g(x) = 2*+2 on the same
Solve f(x) = 3. What point is on the graph of f?
(e Solve g(x) = 4. What point is on the graph of g?
Solve f(x) = g(x). Do the graphs of f and g intersect?
Cartesian plane.
(b) Shade the region bounded by the y-axis, f(x) = 2**1,
and g(x) = 2x+2 on the graph drawn in part (a).
(c) Solve f(x) = g(x) and label the point of intersection
on the graph drawn in part (a).
(c)
If so, where?
(d) Solve (f + g) (x) = 7.
(e) Solve (f – 8) (x) = 2.
& (x) = log3 (x + 5) and g (x) = log3 (x - 1).
(2) Solve f(x) = 2. What point is on the graph of f?
6) Solve g (x) = 3. What point is on the graph of g?
(6) Solve f(x) = g(x). Do the graphs of f and g intersect?
If so, where?
(d) Solve (f + g) (x) = 3.
(e) Solve (f – g) (x) = 2.
8. (a) If f(x) = 3**1 and g(x) = 2**2, graph f and g on the
same Cartesian plane.
(b) Find the point(s) of intersection of the g:ss of fand g
by solving f(x) = g(x). Round areters to three
decimal places. Label any intersection points on the
graph drawn in part (a).
(c) Based on the graph, solve f(x) > g(x}.
* (0) If f(x) = 5*-1 and g(x) = 2*+1 graph f and g on the
same Cartesian plane.
O Find the point(s) of intersection of the graphs of f and g
by solving f(x) = g(x). Label any intersection points
on the graph drawn in part (a).
O Based on the graph, solve f(x) > g(x). 3 dep
94. (a) Graph f(x) = 3*+1 and g(x) = 3*-2 on the same
Cartesian plane.
(b) Shade the region bounded by the y-axis, f(x)
and g (x) = 3*-2 on the graph drawn in part (a).
(c) Solve f(x) = g(x) and label the point of intersection
on the graph drawn in part (a).
3*+1,
a
95. (a) Graph f(x) = 2* – 4.
(b) Find the zero of f.
(c) Based on the graph, solve f(x) < 0.
96. (a) Graph g(x) = 3* – 9.
(b) Find the zero of g.
(c) Based on the graph, solve g(x) > 0.
97. A Population Model The resident population of the United
States in 2018 was 327 million people and was growing at
a rate of 0.7% per year. Assuming that this growth rate
continues, the model P(t) = 327 (1.007)
the population P (in millions of people) in year t.
(a) According to this model, when will the population of the
United States be 415 million people?
1-2018
represents
a bat MI
s intere (b) According to this model, when will the population of the
United States be 470 million people?
plane.
98. A Population Model The population of the world in 2018
was 7.63 billion people and was growing at a rate
of 1.1% per year. Assuming that this growth rate continues,
the model P(t) = 7.63(1.011)-2018 represents the
population P (in billions of people) in year t.
(a) According to this model, when will the population of the
world be 9 billion people?
(b) According to this model, when will the population of the
world be 12.5 billion people?
and g (x) = 10 on the graph drawn in part (a).
on the graph drawn in part (a).
plane.
i the graph drawn in part (a).
Source: U.S. Census Bureau

Transcribed Image Text:3. Approximate the solution(s) to x = x² utility. (pp. B6-B8) 5 using a grupi U LU grapilng utim ) Skill Building In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. 7. log2 (5x) = 4 6. log (x + 6) = 1 log, 15 5. log4 x = 2 dt oto 10. log5(2x + 3) = log, 3 8. log3 (3x – 1) = 2 9. log4 (x + 4) no w d 13. logs 2x – 1| = log5 13 11. log4|x| = 3 12. log2|x 7 = 4 16. -2 log4 x = log4 9 14. log9|3x + 4| = log9|5x – 12| 15. - log7 x = 3 log7 2 19. 2 log6(x - 5) + log, 9 = 2 17. 3 log2 x = -log2 27 18. 2 logs x = 3 log5 4 22. log x + log (x – 21) = 2 20. 2 log3 (x + 4) – log3 9 = 2 21. log x + log (x + 15) = 2 25. log2 (x + 7) + log2(x + 8) = 1| 28. logs (x + 3) = 1 – log3(x – 1) 31. log9 (x + 8) + log,(x + 7) =2 34. log4 (x – 9) – log,(x + 3) = 3 36. log, x + log, (x – 2) = loga(x + 4) 38. log3 x - 2 log3 5 = log3(x + 1) – 2 log; 10 23. log (7x + 6) = 1 + log (x – 1) 24. log (2x) – log (x – 3) = 1 26. logo(x + 4) + log6(x + 3) = 1 27. logs (x + 6) = 1 – logs(x + 4) - 29. In x + In (x + 2) = 4 30. In (x + 1) – In x = 2 32. log2 (x + 1) + log2(x + 7) = 3 33. log1/3 (x + x) – log1/3 (x² – x) = -1 35. log. (x – 1) – log.(x + 6) = loga(x - 2) – loga(x + 3) 37. 2 log5 (x – 3) – log5 8 = log5 2 39. 2 log, (x + 2) = 3 log, 2 + log, 4 40. 3(log7 x – log, 2) = 2 log, 4 41. 2 log13 (x + 2) = log13(4x + 7) deups latnonogx 43. (log3 x)2 – 3log3x = 10 i booubo 42. log (x – 1) = log 2 44. In x - 3V In x + 2 = 0 Bob mo ghbiozerc pe aojogo

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43. (log3 x)2 - 3log3 x = 10 noituloe adi aamizoq