Exponential Growth

Exponential Growth
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2016-07-13 05:23
This example demonstrates exponential growth. It involves the core mathematical concept of exponential functions. Using GeoGebra commands such as PolyLine, Segment, Sequence, etc., the example constructs an exponential growth graph. Suitable for high school math education or learning.

GeoGebra Commands & Parameters

  1. Textfield(ST) → TxtST
  2. Textfield(ET) → TxtET
  3. Textfield(SA) → TxtSA
  4. Textfield(SB) → TxtSB
  5. Textfield(SC) → TxtSC
  6. Textfield(vA) → TxtvA
  7. Textfield(vB) → TxtvB
  8. Textfield(vC) → TxtvC
  9. LaTeX(vA, false, false) → TextvA
  10. LaTeX(vB, false, false) → TextvB
  11. LaTeX(vC, false, false) → TextvC
  12. First(Sequence[(Element[L_T, i + 1], Element[L_A, i + 1]), i, 0, n + 1], Iteration + 1) → L_{TAE}
  13. PolyLine(L_{TAE}) → Str_{AE}
  14. PolyLine(L_{TBE}) → Str_{BE}
  15. PolyLine(L_{TCE}) → Str_{CE}
  16. Element(L_A, Iteration + 1) → Bestand_A
  17. Element(L_B, Iteration + 1) → Bestand_B
  18. Element(L_C, Iteration + 1) → Bestand_C
  19. Element(L_{vA}, Iteration) → Aenderung_A
  20. Element(L_{vB}, Iteration) → Aenderung_B
  21. Element(L_{vC}, Iteration) → Aenderung_C
  22. First(Sequence[(Element[L_T, i + 1], Element[L_{vA}, i + 1]), i, 0, n], Iteration) → L_{TvAE}
  23. PolyLine(L_{TvAE}) → Str_{vAE}
  24. PolyLine(L_{TvBE}) → Str_{vBE}
  25. PolyLine(L_{TvCE}) → Str_{vCE}
  26. Element(L_{TCE}, Iteration) → DrA
  27. Element(L_{TCE}, Iteration + 1) → DrC
  28. Polygon(DrA, DrB, DrC) → Dreieck_C, dr3, dr2, dr1
  29. Element(L_{TvCE}, Iteration) → vCE
  30. Segment(TX, vCE) → Strecke_{vC}
  31. Sequence((Element[L_T, i + 1], Element[L_A, i + 1]), i, 0, n) → L_{TAG}
  32. Sequence((Element[L_T, i + 1], Element[L_{vA}, i + 1]), i, 0, n - 1) → L_{TvAG}
  33. If(b, 1, 5) → d
  34. PolyLine(L_{TAG}) → Str_{AG}
  35. PolyLine(L_{TvAG}) → Str_{vAG}
  36. PolyLine(L_{TBG}) → Str_{BG}
  37. PolyLine(L_{TvBG}) → Str_{vBG}
  38. PolyLine(L_{TCG}) → Str_{CG}
  39. PolyLine(L_{TvCG}) → Str_{vCG}

AI Drawing Prompt Reference

Draw an exponential growth graph with time axis T, initial value A, growth value B, and final value C. Use PolyLine to connect these points and show the growth from A to C. Use Segment to connect key points and illustrate the growth changes. Generate a series of points with Sequence to show the growth trend over time.
The prompt above was compiled from the original drawing commands and is for reference only.