Half-Life

Initial Amount =

Half Life =

Initial Amount

How Much Left ?

half life

half life

half life

Slide Me Slowly!

half-life

half-life

half-life

half-life

Reset

Half-Life Function   

a_0 = 1101.1029549013622 (slider from 0 to 100000, step 0.1)
k = 280 (slider from 0 to 1000, step 0.1)
InputBox1 = Textfield(a_0)
InputBox2 = Textfield(k)
A(x) = (a_0 * (1 / 2)^(x / k))
B: (0, a_0)
text1: "A(x)=" + (LaTeX[A]) + ""
a: y = y(B)
b: y = (1 / 2 * y(B))
c: y = (1 / 4 * y(B))
d: y = (1 / 8 * y(B))
e: y = (1 / 16 * y(B))
D = Intersect(A, b, (280, 550.5514774506811))
E = Intersect(A, c, (560, 275.27573872534055))
F = Intersect(A, d, (840, 137.63786936267027))
G = Intersect(A, e, (1120, 68.81893468133514))
f = 285.1862594650218 (slider from 0 to a_0, step 0.1)
InputBox3 = Textfield(f)
g: y = f
C: (f, A(f))
h: x = 0
H = Intersect(b, h)
i = Segment(H, D)
j: x = x(D)
I = Intersect(c, j)
l: x = x(E)
J = Intersect(d, l)
m = Segment(I, E)
n = Segment(J, F)
p = Segment(D, I)
q = Segment(E, J)
r: x = x(C)
s: y = y(C)
t: y = 0
K = Intersect(h, s)
L = Intersect(r, t)
f_1 = Segment(K, C)
g_1 = Segment(C, L)
M: (0, 0)
N = Midpoint(M, B)
O: (x(D), 0)
P: (x(E), 0)
Q: (x(F), 0)
o = 7.84 (slider from 0 to 20.5, step 0.01)
M' = Dilate(M, If[0 < o ≤ 1, 1 - o, 0], N)
M'_1 = Rotate(M, If[1 < o ≤ 2, ((o - 1) * π), π], N)
M'' = Rotate(M', If[1 < o ≤ 2, ((o - 1) * π), π], N)
N' = Dilate(N, If[2 < o ≤ 3, 3 - o, 0], D)
j_1 = Segment(N, N')
R = Midpoint(D, O)
B' = Dilate(B, If[0 < o ≤ 1, 1 - o, 0], N)
h_1 = Segment(B, B')
B'_1 = Rotate(B, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], N)
B'' = Rotate(B', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], N)
i_1 = Segment(B'_1, B'')
D' = Dilate(D, If[3 < o ≤ 4, 4 - o, 0], R)
k_1 = Segment(D, D')
R' = Dilate(R, If[4 < o ≤ 5, 5 - o, 0], O)
l_1 = Segment(R, R')
D'_1 = Rotate(D, If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], R)
D'' = Rotate(D', If[5 < o ≤ 6, ((-(o - 5)) * π), (-π)], R)
m_1 = Segment(D'_1, D'')
N'_1 = Rotate(N, If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], D)
N'' = Rotate(N', If[6 < o ≤ 7, ((-(o - 6)) * π), (-π)], D)
n_1 = Segment(N'_1, N'')
D'_2 = Dilate(D, If[7 < o ≤ 8, 8 - o, 0], R)
u = Vector(D, D'_2)
S = Translate(N'_1, u)
N''' = Translate(N'', u)
p_1 = Segment(S, N''')
T = Midpoint(P, E)
E' = Dilate(E, If[8 < o ≤ 9, 9 - o, 0], T)
q_1 = Segment(E, E')
T' = Dilate(T, If[9 < o ≤ 10, 10 - o, 0], P)
r_1 = Segment(T, T')
E'_1 = Rotate(E, If[10 < o ≤ 11, ((-(o - 10)) * π), (-π)], T)
E'' = Rotate(E', If[10 < o ≤ 11, ((-(o - 10)) * π), (-π)], T)
s_1 = Segment(E'_1, E'')
S' = Rotate(S, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], E)
U = Rotate(N''', If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], E)
t_1 = Segment(S', U)
E'_2 = Dilate(E, If[12 < o ≤ 13, 13 - o, 0], T)
v = Vector(E, E'_2)
S'' = Translate(S', v)
U' = Translate(U, v)
a_1 = Segment(S'', U')
V = Midpoint(F, Q)
F' = Dilate(F, If[13 < o ≤ 14, 14 - o, 0], V)
b_1 = Segment(F, F')
V' = Dilate(V, If[14 < o ≤ 15, 15 - o, 0], Q)
c_1 = Segment(V, V')
F'_1 = Rotate(F, If[15 < o ≤ 16, ((-(o - 15)) * π), (-π)], V)
F'' = Rotate(F', If[15 < o ≤ 16, ((-(o - 15)) * π), (-π)], V)
d_1 = Segment(F'_1, F'')
S''' = Rotate(S'', If[16 < o ≤ 17, ((-(o - 16)) * π), (-π)], F)
U'' = Rotate(U', If[16 < o ≤ 17, ((-(o - 16)) * π), (-π)], F)
e_1 = Segment(S''', U'')
F'_2 = Dilate(F, If[17 < o ≤ 18, 18 - o, 0], V)
w = Vector(F, F'_2)
W = Translate(S''', w)
U''' = Translate(U'', w)
f_2 = Segment(W, U''')
U'''_1 = Translate(U'', w)
o_1 = Integral(A, 0, Infinity)
g_2 = Ray((0, 0), (1, 0))