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Dynamic Half-Life Function Demo

Dynamic Half-Life Function Demo
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2019-06-27 00:15
FunctionCoordinate GeometryCalculusGraphing
In collections Exploring Exponential & Logarithmic Functions Exploring Exponential & Logarithmic Functions
This example dynamically illustrates the half-life function with interactive parameter adjustments. It covers core math concepts like function graphing, linear equations, ellipses, median values, and calculus operations. Constructed using GeoGebra commands such as Textfield, Intersect, Segment, Midpoint, Dilate, Rotate, Vector, Translate, Ray, and Integral for precise calculations and interactivity. Suitable for high school and above mathematics education, focusing on function analysis, parameter influence exploration, and calculus applications.

GeoGebra Commands & Parameters

  1. Textfield(a_0) → InputBox1
  2. Textfield(k) → InputBox2
  3. Intersect(A, b, (314.9999999999856, 600.0000000000189)) → D
  4. Intersect(A, c, (629.9999999999546, 300.00000000002996)) → E
  5. Intersect(A, d, (944.9999999999218, 150.0000000000258)) → F
  6. Intersect(A, e, (1259.999999999898, 75.00000000001685)) → 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, Initial) → 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(Initial, If[0 < o ≤ 1, 1 - o, 0], N) → B'
  28. Segment(Initial, B') → h_1
  29. Rotate(Initial, 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. Textfield(u_1) → InputBox4
  82. Textfield(val) → InputBox5
  83. Integral(A, 0, (50 * k)) → o_1