I came across this video in my Google+ excursions today and found in it an interesting thought experiment along with an intriguing story related to invention of chess, both pertaining to exponential growths.
The following story has been taken from Wikipedia
When the creator of the game of chess (in some tellings an ancient Indian Brahmin mathematician named Sessa or Sissa) showed his invention to the ruler of the country, the ruler was so pleased that he gave the inventor the right to name his prize for the invention. The man, who was very clever, asked the king this: that for the first square of the chess board, he would receive one grain of wheat (in some tellings, rice), two for the second one, four on the third one, and so forth, doubling the amount each time. The ruler, arithmetically unaware, quickly accepted the inventor's offer, even getting offended by his perceived notion that the inventor was asking for such a low price, and ordered the treasurer to count and hand over the wheat to the inventor. However, when the treasurer took more than a week to calculate the amount of wheat, the ruler asked him for a reason for his tardiness. The treasurer then gave him the result of the calculation, and explained that it would take more than all the assets of the kingdom to give the inventor the reward. The story ends with the inventor being beheaded. (In other variations of the story, the inventor becomes the new king.
The moral of the story: none, because it was for fun.
image source: here