Ever since you were a baby, your family was probably saying: „Look how fast you’re growing! “ Do we really grow as fast as our families think?

The average length of a newborn baby is 50 cm. In the first year of life, on average, it increases its length by 2 cm per month. How tall is the baby on its first birthday?

50+2+2+2+2+2+2+2+2+2+2+2+2=74 cm

Mathematicians call this type of growth **linear growth** and they do not consider it to be particularly fast. When we say that something is growing fast, we most often think about exponential growth.

If the baby’s growth were exponential, the situation would be „a bit“ different. Imagine this!

The average length of a newborn baby is 50 cm. In the first year of life, on average, it increases its length 2 times per month. How tall is the baby on its first birthday?

=204 800cm

Now that is a really fast growth!

Interesting fact: Although babies, luckily, don’t grow fast, there are many examples of exponential growth in nature (for example, the growth of some algae).

Read the following story and find out more about exponential growth!

### The legend of the origin of chess

There are a number of legends about the origin of chess. The best-known among them is the story of Grand Vizier Sissa Ben Dahir and Shirham, a young despot king who oppressed his people. To teach the king that there can be no rule without people, Sissa Ben Dahir invented the game of chess to show that even the weakest figure – the pawn – can decide the outcome of the battle on 64 squares of the game and bring victory. The king quickly learned how to move the pieces and was pleased by the game, and he offered the Grand Vizier any reward he wants. Sissa Ben Dahir had a seemingly very modest request – some wheat. More precisely, one grain of wheat for the first square of the chessboard, two grains for the second square, four for the third square and so on, the number of grains of wheat doubling for each following square. The king thought that the requested amount of wheat would be insignificant and suggested to Sissa to ask for something more valuable. However, the Grand Vizier did not change his mind. Later, the king was very surprised when he was told that there is not enough wheat in the entire world to fulfil the wish of Sissa Ben Dahir.

#### How many grains of wheat was the king supposed to give to Sissa Ben Dahir?

18.446.744.073.709.551.615 grains!