2024 AMC 10A Problem 10

Consider the following operation. Given a positive integer n, if n is a multiple of 3, then you replace n by \frac{n}{3}. If n is not a multiple of 3, then you replace n by n+10. For example, beginning with n=4, this procedure gives 4\to14\to24\to8\to18\to6\to2\to12\to\cdots. Suppose you start with n=100. What value results if you perform this operation exactly 100 times?

\textbf{(A) }10\qquad\textbf{(B) }20\qquad\textbf{(C) }30\qquad\textbf{(D) }40\qquad\textbf{(E) }50

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.