B4. Dijakom, who are looking for temporary employment, wish to offer as many different jobs as possible in the youth service. Therefore, they have decided to double the number of employers offering jobs over the next five years. Each year, they will increase the number of employers by the same percentage. Calculate by what percentage they will increase the number of employers each year. Round the result to the nearest whole number of percentages. Write down your answer.

## Solutions to the problems and scoring guide

## A contestant who has arrived at the correct solution by any valid method (even if not anticipated by the scoring guide) receives all possible points.

For a correct method, any procedure that

- sensibly takes into account the wording of the problem,
- leads to a solution of the problem,
- is mathematically correct and complete.

A contestant who has only partially solved the problem, from otherwise correct solving procedures but does not show the path to the final solution of the problem, cannot receive more than half of the possible points.

## First Year

I. PART

| Problem | 1 | 2 | 3 | 4 | 5 | 6 |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: |
| Answer | $\mathrm{A}$ | $\mathrm{E}$ | $\mathrm{A}$ | $\mathrm{C}$ | $\mathrm{B}$ | $\mathrm{E}$ |
B4. Denimo, that currently offers work through the youth service of $n$ employers. In 5 years, the number of employers will be $2 n$. Let $r$ be the annual growth factor of the number of employers and $r=1+\frac{p}{100}$. The relationship $2 n=n \cdot r^{5}$ holds, from which we get $r=\sqrt[5]{2}$, which is approximately 1.149. From this value, we calculate $p$, which is $p=14.9$ or $p=15$ if rounded to the nearest whole number. Each year, the number of employers will increase by $15 \%$.

![](https://cdn.mathpix.com/cropped/2024_06_07_8d4f73ada7862f989e67g-16.jpg?height=57&width=1641&top_left_y=2136&top_left_x=276)

![](https://cdn.mathpix.com/cropped/2024_06_07_8d4f73ada7862f989e67g-16.jpg?height=60&width=1639&top_left_y=2192&top_left_x=274)

![](https://cdn.mathpix.com/cropped/2024_06_07_8d4f73ada7862f989e67g-16.jpg?height=57&width=1639&top_left_y=2236&top_left_x=274)

![](https://cdn.mathpix.com/cropped/2024_06_07_8d4f73ada7862f989e67g-16.jpg?height=60&width=1639&top_left_y=2283&top_left_x=274)

The calculated and rounded value of the annual increase in percentage $p=15 \% \ldots \ldots . .1$ point

Answer . .................................................................................................................