\section*{Task 1 - 021121}

At the international symposium in Moscow on problems of higher technical and humanistic education, Soviet Nobel laureate Nikolai Semenov explained that with the growth rate achieved in the USSR, the annual production of electricity could be increased to 10,000 times its current level in 100 years.

a) What annual increase (in percent) underlies this perspective?

b) How great was the average annual increase (in percent) in electricity production in the USSR from 1955 to 1961? (In 1955, 170 billion kWh were produced, and in 1961, a total of 327 billion kWh were produced.)

Compare the results!
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a) If the energy production \(E\) has a constant annual growth rate \(x\), the equation becomes \(10000 E=E \cdot(1+x)^{100}\).

The solution is \(x=\sqrt[100]{10000}-1=9.65 \%\).

b) The equation is: \(327=170 \cdot(1+y)^{6}\).

The solution is \(y=\sqrt[6]{\frac{327}{170}}-1=11.53 \%\).

Comparison:

\(y>x\), the actual growth rate is greater than the assumed one.