\section*{Task 2 - 141012}

A VEB has planned to produce 10,000 units of its main product for the year 1975. Furthermore, it is planned to increase the production figures for the years 1976, 1977, 1978, and 1979 so that the figure planned for 1979 reaches four times the value of the figure for 1975. The percentage increase from year to year should be the same for all four years.

a) What is the annual increase in percent, rounded to the nearest whole number, i.e., without considering decimal places?

b) Provide the (correspondingly rounded) production figures for the years 1976, 1977, 1978, and 1979!
}

Using the compound interest formula, we get \(P_{1979}=P_{1975} \cdot(1+p)^{4}\). This, with \(P_{1979}=4 \cdot P_{1975}\), after rearrangement, gives: \(p=\sqrt[4]{4}-1=\sqrt{2}-1\) the value \(p=0.41=41 \%\).

Thus, it follows:

\[
\begin{aligned}
& P_{1976}=P_{1975} \cdot 1.41=14142 \text { pieces } \quad P_{1977}=P_{1976} \cdot 1.41=20000 \text { pieces } \\
& P_{1978}=P_{1977} \cdot 1.41=28283 \text { pieces } \quad P_{1979}=P_{1978} \cdot 1.41=40000 \text { pieces }
\end{aligned}
\]