dice's decay constant 20

2 methods.

1. QUITE COMPLICATED
Plot the graph [no. of dice] against [time].
find the half life, t --- time taken from 100 to 50 OR time taken from 50 to 25 and it should be the same.
decay constant = ln 2 / t.


2. EASIER
Plot the graph ln[no. of dice] against [time].
A straight line can be found.
We can then find the decay constant by considering the -slope.

簡單的說:

1) Calculate the fractional decay for each roll by dividing the number of “decays” per roll by the number of dice rolled.

2) Average the fractional decays to get your decay constant

例如:

time dice left
0 100
1 81

即是, 第一次擲骰子之後, fractional decay 等於 (100 - 81) / 100 = 0.19

因此,

time dice left decays fractional decays
0 100
1 81 19 0.1900
2 67 14 0.1728
3 56 11 0.1642
4 49 7 0.1250
5 37 12 0.2449
6 33 4 0.1081
7 29 4 0.1212
8 24 5 0.1724
9 18 6 0.2500
10 16 2 0.1111
11 12 4 0.2500
12 9 3 0.2500
13 8 1 0.1111
14 7 1 0.1250
15 5 2 0.2857
16 5 0 0.0000
17 3 2 0.4000
18 3 0 0.0000
19 2 1 0.3333
20 1 1 0.5000
21 1 0 0.0000
22 0 1 1.0000

而 decay constant 等於 fractional decays 平均值 0.2234