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Logarithmic Function and Time Relationship

Logarithmic Function and Time Relationship
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2022-01-30 18:27
FunctionSolid GeometryCalculusLimitGraphing
This example dynamically demonstrates the logarithmic function's behavior over time, showcasing its growth pattern. Key math concepts include logarithmic functions, limits, solids in solid geometry, and percentage calculations. GeoGebra commands like Sequence, Point, and Segment are used to construct the function graph and geometric shapes. Suitable for high school and above learners to understand the application and visualization of logarithmic functions.

GeoGebra Commands & Parameters

  1. Sequence(Segment[(k, 0), (k, 0.5)], k, -10, 10) → l1, {0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5}
  2. Sequence((log(10, k), 0), k, 1, 9) → l2, {(0, 0), (0.30102999566398114, 0), (0.47712125471966244, 0), (0.6020599913279623, 0), (0.6989700043360187, 0), (0.7781512503836435, 0), (0.8450980400142567, 0), (0.9030899869919434, 0), (0.9542425094393249, 0)}
  3. Sequence(Translate[l2, Vector[(0, 0), (k, 0)]], k, -10, 9) → m1, {{(-10, 0), (-9.698970004336019, 0), (-9.522878745280337, 0), (-9.397940008672037, 0), (-9.301029995663981, 0), (-9.221848749616356, 0), (-9.154901959985743, 0), (-9.096910013008056, 0), (-9.045757490560675, 0)}, {(-9, 0), (-8.698970004336019, 0), (-8.522878745280337, 0), (-8.397940008672037, 0), (-8.301029995663981, 0), (-8.221848749616356, 0), (-8.154901959985743, 0), (-8.096910013008056, 0), (-8.045757490560675, 0)}, {(-8, 0), (-7.698970004336019, 0), (-7.522878745280337, 0), (-7.3979400086720375, 0), (-7.301029995663981, 0), (-7.221848749616356, 0), (-7.154901959985743, 0), (-7.096910013008056, 0), (-7.045757490560675, 0)}, {(-7, 0), (-6.698970004336019, 0), (-6.522878745280337, 0), (-6.3979400086720375, 0), (-6.301029995663981, 0), (-6.221848749616356, 0), (-6.154901959985743, 0), (-6.096910013008056, 0), (-6.045757490560675, 0)}, {(-6, 0), (-5.698970004336019, 0), (-5.522878745280337, 0), (-5.3979400086720375, 0), (-5.301029995663981, 0), (-5.221848749616356, 0), (-5.154901959985743, 0), (-5.096910013008056, 0), (-5.045757490560675, 0)}, {(-5, 0), (-4.698970004336019, 0), (-4.522878745280337, 0), (-4.3979400086720375, 0), (-4.301029995663981, 0), (-4.221848749616356, 0), (-4.154901959985743, 0), (-4.096910013008056, 0), (-4.045757490560675, 0)}, {(-4, 0), (-3.6989700043360187, 0), (-3.5228787452803374, 0), (-3.3979400086720375, 0), (-3.3010299956639813, 0), (-3.2218487496163566, 0), (-3.154901959985743, 0), (-3.0969100130080567, 0), (-3.0457574905606752, 0)}, {(-3, 0), (-2.6989700043360187, 0), (-2.5228787452803374, 0), (-2.3979400086720375, 0), (-2.3010299956639813, 0), (-2.2218487496163566, 0), (-2.154901959985743, 0), (-2.0969100130080567, 0), (-2.0457574905606752, 0)}, {(-2, 0), (-1.6989700043360187, 0), (-1.5228787452803376, 0), (-1.3979400086720377, 0), (-1.3010299956639813, 0), (-1.2218487496163566, 0), (-1.1549019599857433, 0), (-1.0969100130080567, 0), (-1.0457574905606752, 0)}, {(-1, 0), (-0.6989700043360189, 0), (-0.5228787452803376, 0), (-0.3979400086720377, 0), (-0.30102999566398125, 0), (-0.22184874961635648, 0), (-0.1549019599857433, 0), (-0.09691001300805657, 0), (-0.04575749056067513, 0)}, {(0, 0), (0.30102999566398114, 0), (0.47712125471966244, 0), (0.6020599913279623, 0), (0.6989700043360187, 0), (0.7781512503836435, 0), (0.8450980400142567, 0), (0.9030899869919434, 0), (0.9542425094393249, 0)}, {(1, 0), (1.3010299956639813, 0), (1.4771212547196624, 0), (1.6020599913279623, 0), (1.6989700043360187, 0), (1.7781512503836434, 0), (1.8450980400142567, 0), (1.9030899869919433, 0), (1.9542425094393248, 0)}, {(2, 0), (2.3010299956639813, 0), (2.4771212547196626, 0), (2.6020599913279625, 0), (2.6989700043360187, 0), (2.7781512503836434, 0), (2.845098040014257, 0), (2.9030899869919433, 0), (2.9542425094393248, 0)}, {(3, 0), (3.3010299956639813, 0), (3.4771212547196626, 0), (3.6020599913279625, 0), (3.6989700043360187, 0), (3.7781512503836434, 0), (3.845098040014257, 0), (3.9030899869919433, 0), (3.9542425094393248, 0)}, {(4, 0), (4.301029995663981, 0), (4.477121254719663, 0), (4.6020599913279625, 0), (4.698970004336019, 0), (4.778151250383644, 0), (4.845098040014257, 0), (4.903089986991944, 0), (4.954242509439325, 0)}, {(5, 0), (5.301029995663981, 0), (5.477121254719663, 0), (5.6020599913279625, 0), (5.698970004336019, 0), (5.778151250383644, 0), (5.845098040014257, 0), (5.903089986991944, 0), (5.954242509439325, 0)}, {(6, 0), (6.301029995663981, 0), (6.477121254719663, 0), (6.6020599913279625, 0), (6.698970004336019, 0), (6.778151250383644, 0), (6.845098040014257, 0), (6.903089986991944, 0), (6.954242509439325, 0)}, {(7, 0), (7.301029995663981, 0), (7.477121254719663, 0), (7.6020599913279625, 0), (7.698970004336019, 0), (7.778151250383644, 0), (7.845098040014257, 0), (7.903089986991944, 0), (7.954242509439325, 0)}, {(8, 0), (8.301029995663981, 0), (8.477121254719663, 0), (8.602059991327963, 0), (8.698970004336019, 0), (8.778151250383644, 0), (8.845098040014257, 0), (8.903089986991944, 0), (8.954242509439325, 0)}, {(9, 0), (9.301029995663981, 0), (9.477121254719663, 0), (9.602059991327963, 0), (9.698970004336019, 0), (9.778151250383644, 0), (9.845098040014257, 0), (9.903089986991944, 0), (9.954242509439325, 0)}}
  4. Point(m1) → P1
  5. Segment(Q1, R1) → i1
  6. Segment(R1, S1) → j1
  7. Sequence(Segment[(log(10, k), 0), (log(10, k), 0.4)], k, 2, 9) → l3, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}
  8. Sequence(Translate[l3, Vector[(0, 0), (k, 0)]], k, -10, 9) → m2, {{0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}}
  9. Segment((x(P1), -2), (x(P1), 2)) → h1'
  10. Point(h1') → P1'
  11. Segment((x(P1), -0.5), (x(P1), 0.8)) → h1
  12. Point(m1) → P2
  13. Segment((x(P2), -0.5), (x(P2), 0.8)) → h2
  14. Segment((x(P2), -2), (x(P2), 2)) → h2'
  15. Segment(Q2, R2) → i2
  16. Segment(R2, S2) → j2
  17. Point(h2') → P2'
  18. Point(m1) → P3
  19. Segment((x(P3), -0.5), (x(P3), 0.8)) → h3
  20. Segment((x(P3), -2), (x(P3), 2)) → h3'
  21. Point(h3') → P3'
  22. Segment(Q3, R3) → i3
  23. Segment(R3, S3) → j3
  24. Point(g) → P4
  25. Segment((x(P4), -0.5), (x(P4), 0.8)) → h4
  26. Segment(Q4, R4) → i4
  27. Segment(R4, S4) → j4

AI Drawing Prompt Reference

Draw a logarithmic function graph from -10 to 10 on the x-axis, with horizontal line segments moving up 0.5 units for each unit on the x-axis. Then, plot points for the function y=log10(x) from x=1 to x=9, and translate these points along the x-axis to form a series of parallel line segments. Next, draw vertical line segments from -2 to 2 on the x-axis and mark points. Finally, draw horizontal line segments from these points to form a trapezoid-like shape.
The prompt above was compiled from the original drawing commands and is for reference only.