13.316. An enterprise increased the volume of its production annually by the same percentage. Find this percentage if it is known that over two years, the volume of production increased by two times.
## Solution.

Let $x$ be the volume of production, and $y$ be the percentage.

In one year, the volume of production becomes $x+\frac{y}{100}=x\left(1+\frac{y}{100}\right)$, and in the second year, it becomes $-x\left(1+\frac{y}{100}\right)+\frac{y}{100}\left(x\left(1+\frac{y}{100}\right)\right)=x\left(1+\frac{y}{100}\right)^{2}$. According to the condition, we have $x\left(1+\frac{y}{100}\right)^{2}=2 x$, from which $y=(\sqrt{2}-1) \cdot 100$ or $y \approx 41.4 \%$. Answer: $\approx 41.4 \%$.