To determine how many hours it will take for the bacterial count to reach 2,048, let's continue the table provided.
From the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time (hours), } x & \text{Bacterial Count} \\
\hline
1 & 2^1 = 2 \\
\hline
2 & 2^2 = 4 \\
\hline
3 & 2^3 = 8 \\
\hline
4 & 2^4 = 16 \\
\hline
5 & 2^5 = 32 \\
\hline
\end{array}
\][/tex]
We need to continue the table until we reach a bacterial count of 2,048:
[tex]\[
\begin{array}{|c|c|}
\hline
6 & 2^6 = 64 \\
\hline
7 & 2^7 = 128 \\
\hline
8 & 2^8 = 256 \\
\hline
9 & 2^9 = 512 \\
\hline
10 & 2^{10} = 1024 \\
\hline
11 & 2^{11} = 2048 \\
\hline
\end{array}
\][/tex]
Therefore, the bacterial count will reach 2,048 after [tex]\( \boxed{11} \)[/tex] hours.
