放射性物质半衰期演示
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①本范例演示放射性物质半衰期与初始量无关的数学现象;②涉及核心概念:半衰期、指数衰减、独立性与数学建模;③作图要点:运用了Textfield, Intersect, Segment, Midpoint, Dilate, Rotate, Integral, Ray, Point, Vector, Translate等GeoGebra命令与对象;④适合高中及以上学生及教师用于理解放射性物质衰减规律及微积分应用。
GeoGebra 命令及参数
Textfield(a_0) → InputBox1Textfield(k) → InputBox2Intersect(A, b, (315.1, 600)) → DIntersect(A, c, (630.2, 300)) → EIntersect(A, d, (945.3000000000001, 150)) → FIntersect(A, e, (1260.4000000000003, 74.99999999999994)) → GTextfield(f) → InputBox3Intersect(b, h) → HSegment(H, D) → iIntersect(c, j) → IIntersect(d, l) → JSegment(I, E) → mSegment(J, F) → nSegment(D, I) → pSegment(E, J) → qIntersect(h, s) → KIntersect(r, t) → LSegment(K, C) → f_1Segment(C, L) → g_1Midpoint(M, Initial) → NDilate(M, If[0 < o ≤ 1, 1 - o, 0], N) → M'Rotate(M, If[1 < o ≤ 2, ((o - 1) * π), π], N) → M'_1Rotate(M', If[1 < o ≤ 2, ((o - 1) * π), π], N) → M''Dilate(N, If[2 < o ≤ 3, 3 - o, 0], D) → N'Segment(N, N') → j_1Dilate(Initial, If[0 < o ≤ 1, 1 - o, 0], N) → B'Segment(Initial, B') → h_1Rotate(Initial, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], N) → B'_1Rotate(B', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], N) → B''Segment(B'_1, B'') → i_1Rotate(N', If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], D) → N''Integral(A, 0, Infinity) → o_1Ray((0, 0), (1, 0)) → g_2Textfield(u_1) → InputBox4Textfield(val) → InputBox5Point(A) → RIntersect(k_1, y = 0) → SMidpoint(R, S) → UIntersect(A, l_1, (747.0739488341455, 231.98826691092705)) → WDilate(R, If[3 < o ≤ 4, 4 - o, 0], U) → R'Segment(R, R') → m_1Dilate(U, If[4 < o ≤ 5, 5 - o, 0], S) → U'Segment(U, U') → n_1Rotate(R, If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], U) → R'_1Rotate(R', If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], U) → R''Segment(R'_1, R'') → p_1Dilate(U, If[6 < o ≤ 7, 7 - o, 0], W) → U'_1Segment(U, U'_1) → t_1Dilate(N, If[7 < o ≤ 8, 8 - o, 0], U) → N'_1Vector(N, N'_1) → uTranslate(N, u) → N'_2Translate(N', u) → N''_1Segment(N'_2, N''_1) → a_1
AI 绘图提示语参考
绘制一个展示放射性物质半生命概念的图形,包含初始量与衰减率的输入框,以及多个交点、线段和中点,通过这些元素构建出半衰期独立的指数衰减曲线,并用积分和向量工具进行数学建模,适合高中学生理解放射性衰减和微积分应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。