13.011. Due to the reconstruction of equipment, the labor productivity of a worker increased twice during the year by the same percentage. By what percentage did the labor productivity increase each time, if during the same time a worker used to produce goods worth 2500 rubles, and now produces goods worth 2809 rubles?
Solution.

Let a worker produce a parts in 8 hours of work. Then the rate is $\frac{2500}{a}$ rubles per part, and the labor productivity is $\frac{a}{8}$ parts per hour. After the first increase in productivity by $x \%$, the worker started producing $\frac{a}{8}+\frac{x \cdot a}{100 \cdot 8}$ parts per hour; after the second increase in productivity by $x \% - \frac{a}{8}\left(1+\frac{x}{100}\right)\left(1+\frac{x}{100}\right)$ parts per hour. In 8 hours, he started producing $a\left(1+\frac{x}{100}\right)^{2}$ parts and earned $a\left(1+\frac{x}{100}\right)^{2} \cdot \frac{2500}{a}$ rubles. According to the condition, $a\left(1+\frac{x}{100}\right)^{2} \cdot \frac{2500}{a}=2809$, from which $x=6 \%$.

Answer: $6 \%$.