Lokium Half-Life Simulation

Trial
Dice Removed Dice Remaining

1
0
60
2
10
50
3
9
41
4

34
5
3
31

4
27
7
3
24
8
3
21
9

16
10
3
13
11
0
13
12

12
2. In the graph above, after which trial was the half-life of Lokium reached? * 2 points (HINT: Trial 1 started with 60 dice)
• Trial 12

Trial 6
Trial 1
Trial 9

1 answer

To determine after which trial the half-life of Lokium was reached, we first need to understand the concept of half-life in this context. The half-life of a substance is the time it takes for half of the original amount to decay.

In this case, starting with 60 dice:

  • After Trial 1: 60 dice (0 removed)
  • After Trial 2: 50 dice (10 removed)
  • After Trial 3: 41 dice (9 removed)
  • After Trial 4: 34 dice (7 removed)
  • After Trial 5: 31 dice (3 removed)
  • After Trial 6: 27 dice (4 removed)
  • After Trial 7: 24 dice (3 removed)
  • After Trial 8: 21 dice (3 removed)
  • After Trial 9: 16 dice (5 removed)
  • After Trial 10: 13 dice (3 removed)
  • After Trial 11: 13 dice (0 removed)
  • After Trial 12: 12 dice (1 removed)

To find the half-life, we look for when the number of remaining dice reaches half of the original count:

  • Original count = 60
  • Half of 60 = 30

Looking through the trials:

  • At Trial 1, there are still 60 dice (not half).
  • At Trial 2, there are 50 dice (still not half).
  • At Trial 3, there are 41 dice (still not half).
  • At Trial 4, there are 34 dice (still not half).
  • At Trial 5, there are 31 dice (still not half).
  • At Trial 6, there are 27 dice (now below half).

Thus, the half-life of Lokium was reached after Trial 5 when 31 dice remain, which is still above that threshold of 30, but after trial 6 when we see a drop below 30 (to 27). Hence, the half-life would effectively be considered to have occurred before Trial 6.

However, based on the options given in your question:

  • Trial 1
  • Trial 6
  • Trial 9
  • Trial 12

None of these options describe it accurately, but the half-life is effectively reached just after Trial 5.

From the choices: None of the options are correct. However, if you adjust it as more of a range, you could argue it is closest to Trial 6 (as the first indication it drops below half).