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3.1 Fundamental Theorem of Calculus: Tracking Bank Account Balance

3.1 Fundamental Theorem of Calculus: Tracking Bank Account Balance
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2019-01-23 09:19
FunctionCalculusIntegral
In collections TFM: Introducción al Cálculo Infinitesimal (1º Bachillerato)
This example demonstrates the Fundamental Theorem of Calculus by tracking a bank account balance. Key mathematical concepts include integration and differentiation. Using GeoGebra commands such as Point, PolyLine, and Segment, a dynamic graph of the changing bank account balance is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point({1, var1}) → AV1
  2. Point({2, var2}) → AV2
  3. Point({3, var3}) → AV3
  4. Point({4, var4}) → AV4
  5. Point({5, var5}) → AV5
  6. Point({6, var6}) → AV6
  7. Point({7, var7}) → AV7
  8. Point({8, var8}) → AV8
  9. Point({9, var9}) → AV9
  10. Point({10, var10}) → AV10
  11. PolyLine(A0, A1, A10, A2, A3, A4, A5, A6, A7, A8, A9) → g
  12. Point({1, y(A0)}) → AUX1
  13. Segment(A0, AUX1) → V1A
  14. Segment(AUX1, A1) → V1B
  15. Point({2, y(A1)}) → AUX2
  16. Segment(A1, AUX2) → V2A
  17. Segment(AUX2, A2) → V2B
  18. Point({3, y(A2)}) → AUX3
  19. Point({4, y(A3)}) → AUX4
  20. Point({5, y(A4)}) → AUX5
  21. Point({6, y(A5)}) → AUX6
  22. Point({7, y(A6)}) → AUX7
  23. Point({8, y(A7)}) → AUX8
  24. Point({9, y(A8)}) → AUX9
  25. Point({10, y(A9)}) → AUX10
  26. Segment(A2, AUX3) → V3A
  27. Segment(AUX3, A3) → V3B
  28. Segment(AUX4, A4) → V4B
  29. Segment(A3, AUX4) → V4A
  30. Segment(A4, AUX5) → V5A
  31. Segment(AUX5, A5) → V5B
  32. Segment(A5, AUX6) → V6A
  33. Segment(AUX6, A6) → V6B
  34. Segment(A6, AUX7) → V7A
  35. Segment(AUX7, A7) → V7B
  36. Segment(A7, AUX8) → V8A
  37. Segment(AUX8, A8) → V8B
  38. Segment(A8, AUX9) → V9A
  39. Segment(AUX9, A9) → V9B
  40. Segment(A9, AUX10) → V10A
  41. Segment(AUX10, A10) → V10B
  42. Point({0, 0}) → P0
  43. Point({1, 0}) → P1
  44. Point({2, 0}) → P2
  45. Point({3, 0}) → P3
  46. Point({4, 0}) → P4
  47. Point({5, 0}) → P5
  48. Point({6, 0}) → P6
  49. Point({7, 0}) → P7
  50. Point({8, 0}) → P8
  51. Point({9, 0}) → P9
  52. Point({10, 0}) → P10
  53. Point({0, y(AV1)}) → PB0
  54. Point({1, y(AV2)}) → PB1
  55. Polygon(P0, PB0, AV1, P1) → ACU1, p0, pb0, av1, p1
  56. Point({2, y(AV3)}) → PB2
  57. Point({3, y(AV4)}) → PB3
  58. Point({4, y(AV5)}) → PB4
  59. Point({5, y(AV6)}) → PB5
  60. Point({6, y(AV7)}) → PB6
  61. Point({7, y(AV8)}) → PB7
  62. Point({8, y(AV9)}) → PB8
  63. Point({9, y(AV10)}) → PB9
  64. PolyLine(AV0, PB0, AV5, PB5, AV6, PB6, AV7, PB7, AV8, PB8, AV9, PB9, AV1, AV10, P10, PB1, AV2, PB2, AV3, PB3, AV4, PB4) → f
  65. Polygon(P1, PB1, AV2, P2) → ACU2, h, pb1, av2, p2
  66. Polygon(P2, PB2, AV3, P3) → ACU3, i, j, k, l
  67. Polygon(P3, PB3, AV4, P4) → ACU4, p3, pb3, av4, p4
  68. Polygon(P4, PB4, AV5, P5) → ACU5, m, pb4, av5, p5
  69. Polygon(P5, PB5, AV6, P6) → ACU6, n, pb5, av6, p6
  70. Polygon(P6, PB6, AV7, P7) → ACU7, p, pb6, av7, p7
  71. Polygon(P7, PB7, AV8, P8) → ACU8, q, pb7, av8, p8
  72. Polygon(P8, PB8, AV9, P9) → ACU9, r, pb8, av9, p9
  73. Polygon(P9, PB9, AV10, P10) → ACU10, s, pb9, av10, p10
  74. Segment(AV3, P3) → av3

AI Drawing Prompt Reference

Draw a dynamic graph showing the change in a bank account balance over time. First, create 10 points representing the balance at different times, then connect these points with a polyline. Next, draw vertical lines from each point to the x-axis to represent the change in balance for each time period. Finally, connect the endpoints of these vertical lines with segments to form a step-like graph, illustrating the change in balance over time.
The prompt above was compiled from the original drawing commands and is for reference only.