To calculate the number of rabbits for each month, we need to follow these steps:
1. Identify the starting values:
- For month 8: There are already 302 rabbits and 13 females that are able to have kits.
- Each month, 6 additional females come of age to have kits.
- Each female produces 12 kits.
2. Calculate the number of rabbits for month 9:
- In month 9, the number of females of age increases by 6, making it [tex]\( 13 + 6 = 19 \)[/tex] females.
- The number of new rabbits produced is [tex]\( 19 \times 12 = 228 \)[/tex].
- The total number of rabbits in month 9 is [tex]\( 302 + 228 = 530 \)[/tex].
3. Calculate the number of rabbits for month 10:
- In month 10, the number of females of age increases by another 6, making it [tex]\( 19 + 6 = 25 \)[/tex] females.
- The number of new rabbits produced is [tex]\( 25 \times 12 = 300 \)[/tex].
- The total number of rabbits in month 10 is [tex]\( 530 + 300 = 830 \)[/tex].
4. Calculate the number of rabbits for month 11:
- In month 11, the number of females of age increases by another 6, making it [tex]\( 25 + 6 = 31 \)[/tex] females.
- The number of new rabbits produced is [tex]\( 31 \times 12 = 372 \)[/tex].
- The total number of rabbits in month 11 is [tex]\( 830 + 372 = 1202 \)[/tex].
5. Calculate the number of rabbits for month 12:
- In month 12, the number of females of age increases by another 6, making it [tex]\( 31 + 6 = 37 \)[/tex] females.
- The number of new rabbits produced is [tex]\( 37 \times 12 = 444 \)[/tex].
- The total number of rabbits in month 12 is [tex]\( 1202 + 444 = 1646 \)[/tex].
So, the results fill the blank spaces in the table as follows:
[tex]\[
\begin{tabular}{l|l}
Month & Rabbits \\
\hline
1 & 2 \\
2 & 14 \\
3 & 26 \\
4 & 38 \\
5 & 50 \\
6 & 62 \\
7 & 146 \\
8 & 302 \\
9 & 530 \\
10 & 830 \\
11 & 1202 \\
12 & 1646 \\
\end{tabular}
\][/tex]
