To solve the problem step-by-step according to the data provided, let's fill in the blanks with the given results.
1. Cycle 2:
- Initial Atoms: 50
- Simulated Result (A): 25
2. Cycle 3:
- Initial Atoms: 25
- Simulated Result (B): 12
3. Cycle 4:
- Initial Atoms: 13
- Simulated Result (C): 7
4. Cycle 5:
- Initial Atoms: 3
- Simulated Result (D): -1
5. Cycle 6:
- Initial Atoms: 2
- Simulated Result (F): -1
6. Cycle 7:
- Initial Atoms: 1
- Simulated Result (H): -1
So, our results would be:
[tex]$
\begin{array}{l}
A = 25 \\
B = 12 \\
C = 7 \\
D = -1 \\
E \\
F = -1 \\
G \\
H = -1
\end{array}
$[/tex]
Now, our table of data should look like this:
\begin{tabular}{|c|c|c|}
\hline \multirow{2}{*}{\begin{tabular}{c}
Time-Half-Life \\
Cycles, [tex]$n$[/tex]
\end{tabular}} & \multicolumn{2}{|c|}{ Radioactive Atoms } \\
\cline { 2 - 3 } Initial & Predicted & Simulated \\
\hline 1 & 100 & 100 \\
\hline 2 & 50 & 25 \\
\hline 3 & 25 & 12 \\
\hline 4 & 13 & 7 \\
\hline 5 & 3 & -1 \\
\hline 6 & 2 & -1 \\
\hline 7 & 1 & -1 \\
\hline 8 & 0 & \\
\hline
\end{tabular}
