Spivak $A . B$.

Over two years, the factory reduced the volume of its production by $51 \%$. Each year, the volume of production decreased by the same percentage. By how much?
If the volume of production has decreased by $51 \%$, it means that it has become $49 \%$ of the initial volume, and $49=7^{2}$.

## Solution

Let the production decrease by $x \%$ per year. Taking the initial volume of production as 1, we get that after one year, the production volume is

$\alpha=1-x / 100$, and after two years, it is $-\alpha^{2}$. From this, $\alpha^{2}=1-0.51=0.49$, that is, $\alpha=0.7$.

## Answer

By $30 \%$.