11. A fish farm raises fish, in the first year, the growth rate of the fish's weight is $200\%$, and it is expected that the growth rate in subsequent years will be 0.5 times the previous year's growth rate.
（1）After 5 years of breeding, how many times the original weight is the fish's weight expected to be?
（2）If due to environmental pollution, the fish's weight decreases by $10\%$ each year, then after how many years will the total weight of the fish start to gradually decrease?
11. (1) Let the weight of the fish at the end of the $n$-th year be $a_{n}$. According to the problem, the growth rate forms a geometric sequence with the first term 2 and common ratio $\frac{1}{2}$. Therefore, the growth rate in the $n$-th year is $\left(\frac{1}{2}\right)^{n-2}$, and $a_{n}=a_{n-1}\left[1+\left(\frac{1}{2}\right)^{n-2}\right], a_{1}=3 a_{0}, \cdots, a_{5}=\frac{405}{32} a_{0}$.
$a_{0}$ represents the original weight of the fish, so the expected weight of the fish after 5 years is $\frac{405}{32}$ times the original weight;
(2) Let the total weight of the fish at the end of the $n$-th year be $a_{n}$, and the total weight of the fish starts to decrease, then
$$
a_{n+1}=a_{n}\left[1+\left(\frac{1}{2}\right)^{n-1}\right] \cdot \frac{9}{10}, a_{n}=\left[1+\left(\frac{1}{2}\right)^{n-2}\right] a_{n-1} \cdot \frac{9}{10} .
$$

From the condition, we have $a_{n+1}<a_{n}$, and $a_{n-1} \leqslant a_{n}$, solving this gives $18<2^{n} \leqslant 36$, so $n=5$, meaning the total weight of the fish starts to decrease after the 5th year.