13.48 Assume that at the end of a year, a unit of money has depreciated by $10 \%$ compared to the beginning of the year. Find the smallest integer $n$ such that after $n$ years, a unit of money has depreciated by at least $90 \%$. $n$ is (the value of $\lg 3$ to three decimal places is 0.477)
(A) 14.
(B) 16.
(C) 18.
(D) 20.
(E) 22.
(32nd American High School Mathematics Examination, 1981)
［Solution］Let $A$ represent the value of a unit of money at the beginning, then $0.9 A$ represents its value after one year, and $(0.9)^{n} A$ represents its value after $n$ years. We only need to find the smallest positive integer $n$ such that
$$
(0.9)^{n} A \leqslant 0.1 A \text {, i.e., }\left(\frac{9}{10}\right)^{n} \leqslant \frac{1}{10} \text {. }
$$

Thus, $\lg \left(\frac{9}{10}\right)^{n} \leqslant \lg \frac{1}{10}$,
which means
$$
\begin{aligned}
n(2 \lg 3-1) \leqslant-1 . \\
\therefore \quad n \geqslant \frac{1}{1-2 \lg 3} \approx 21.7 .
\end{aligned}
$$

Therefore, the answer is $(E)$.