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Half-Life Dynamic Demonstration

Half-Life Dynamic Demonstration
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2019-06-27 00:17
FunctionCalculusTransformation
In collections Exploring Exponential & Logarithmic Functions Exploring Exponential & Logarithmic Functions
This example demonstrates the dynamic process of an element's half-life, involving exponential functions. By adjusting parameters, observe the changes in half-life. It uses GeoGebra commands such as Textfield, Intersect, Segment, etc., suitable for high school and above students to learn about exponential functions and their applications.

GeoGebra Commands & Parameters

  1. Textfield(a_0) → InputBox1
  2. Textfield(k) → InputBox2
  3. Intersect(A, b, (475.00000000000006, 608.7077589414912)) → D
  4. Intersect(A, c, (950, 304.35387947074565)) → E
  5. Intersect(A, d, (1425, 152.17693973537283)) → F
  6. Intersect(A, e, (1900, 76.08846986768641)) → G
  7. Textfield(f) → InputBox3
  8. Intersect(b, h) → H
  9. Segment(H, D) → i
  10. Intersect(c, j) → I
  11. Intersect(d, l) → J
  12. Segment(I, E) → m
  13. Segment(J, F) → n
  14. Segment(D, I) → p
  15. Segment(E, J) → q
  16. Intersect(h, s) → K
  17. Intersect(r, t) → L
  18. Segment(K, C) → f_1
  19. Segment(C, L) → g_1
  20. Midpoint(M, B) → N
  21. Dilate(M, If[0 < o ≤ 1, 1 - o, 0], N) → M'
  22. Rotate(M, If[1 < o ≤ 2, ((o - 1) * π), π], N) → M'_1
  23. Rotate(M', If[1 < o ≤ 2, ((o - 1) * π), π], N) → M''
  24. Dilate(N, If[2 < o ≤ 3, 3 - o, 0], D) → N'
  25. Segment(N, N') → j_1
  26. Midpoint(D, O) → R
  27. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], N) → B'
  28. Segment(B, B') → h_1
  29. Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], N) → B'_1
  30. Rotate(B', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], N) → B''
  31. Segment(B'_1, B'') → i_1
  32. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], R) → D'
  33. Segment(D, D') → k_1
  34. Dilate(R, If[4 < o ≤ 5, 5 - o, 0], O) → R'
  35. Segment(R, R') → l_1
  36. Rotate(D, If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], R) → D'_1
  37. Rotate(D', If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], R) → D''
  38. Segment(D'_1, D'') → m_1
  39. Rotate(N, If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], D) → N'_1
  40. Rotate(N', If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], D) → N''
  41. Segment(N'_1, N'') → n_1
  42. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], R) → D'_2
  43. Vector(D, D'_2) → u
  44. Translate(N'_1, u) → S
  45. Translate(N'', u) → N'''
  46. Segment(S, N''') → p_1
  47. Midpoint(P, E) → T
  48. Dilate(E, If[8 < o ≤ 9, 9 - o, 0], T) → E'
  49. Segment(E, E') → q_1
  50. Dilate(T, If[9 < o ≤ 10, 10 - o, 0], P) → T'
  51. Segment(T, T') → r_1
  52. Rotate(E, If[10 < o ≤ 11, ((-(o - 10)) * π), (-π)], T) → E'_1
  53. Rotate(E', If[10 < o ≤ 11, ((-(o - 10)) * π), (-π)], T) → E''
  54. Segment(E'_1, E'') → s_1
  55. Rotate(S, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], E) → S'
  56. Rotate(N''', If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], E) → U
  57. Segment(S', U) → t_1
  58. Dilate(E, If[12 < o ≤ 13, 13 - o, 0], T) → E'_2
  59. Vector(E, E'_2) → v
  60. Translate(S', v) → S''
  61. Translate(U, v) → U'
  62. Segment(S'', U') → a_1
  63. Midpoint(F, Q) → V
  64. Dilate(F, If[13 < o ≤ 14, 14 - o, 0], V) → F'
  65. Segment(F, F') → b_1
  66. Dilate(V, If[14 < o ≤ 15, 15 - o, 0], Q) → V'
  67. Segment(V, V') → c_1
  68. Rotate(F, If[15 < o ≤ 16, ((-(o - 15)) * π), (-π)], V) → F'_1
  69. Rotate(F', If[15 < o ≤ 16, ((-(o - 15)) * π), (-π)], V) → F''
  70. Segment(F'_1, F'') → d_1
  71. Rotate(S'', If[16 < o ≤ 17, ((-(o - 16)) * π), (-π)], F) → S'''
  72. Rotate(U', If[16 < o ≤ 17, ((-(o - 16)) * π), (-π)], F) → U''
  73. Segment(S''', U'') → e_1
  74. Dilate(F, If[17 < o ≤ 18, 18 - o, 0], V) → F'_2
  75. Vector(F, F'_2) → w
  76. Translate(S''', w) → W
  77. Translate(U'', w) → U'''
  78. Segment(W, U''') → f_2
  79. Translate(U'', w) → U'''_1
  80. Ray((0, 0), (1, 0)) → g_2
  81. Integral(A, 0, (50 * k)) → o_1

AI Drawing Prompt Reference

Create a diagram illustrating the dynamic process of an element's half-life. Include an exponential decay curve, with several equally spaced vertical lines intersecting the curve at points that drop down to the horizontal axis, forming a series of decreasing-height bars. Add adjustable input fields or sliders below the curve to control the initial amount and decay constant. Also incorporate auxiliary line segments and animated rotation/scaling effects to simulate particle movement during nuclear decay, with a clear layout for observing half-life changes.
The prompt above was compiled from the original drawing commands and is for reference only.