A researcher analyzed the data on the number of new cases of a disease in a city over a period of 5 consecutive years and organized them in the table below.
YearNew cases
1200
2400
3800
41600
53200

Based on this data, the researcher modeled the number of new cases as a function of the year $x$ by the expression $f(x) = 100 \cdot 2^x$.
If this trend continues, in which year will the number of new cases first exceed 100,000?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
A researcher analyzed the data on the number of new cases of a disease in a city over a period of 5 consecutive years and organized them in the table below.

\begin{center}
\begin{tabular}{|c|c|}
\hline
Year & New cases \\
\hline
1 & 200 \\
2 & 400 \\
3 & 800 \\
4 & 1600 \\
5 & 3200 \\
\hline
\end{tabular}
\end{center}

Based on this data, the researcher modeled the number of new cases as a function of the year $x$ by the expression $f(x) = 100 \cdot 2^x$.

If this trend continues, in which year will the number of new cases first exceed 100,000?

\noindent(A) 9\\
(B) 10\\
(C) 11\\
(D) 12\\
(E) 13