Exponential+Growth

**Exponential growth** occurs when the growth rate of the value of a mathematical function is proportional to the function's current value. In the case of a discrete domain of definition with equal intervals it is also called geometric growth. The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth. 


 * The Story of Exponential growth- Rice on a chessboard **

According to legend, vizier Sissa Ben Dahir presented an Indian King Sharim with a beautiful, hand-made chessboard.The king asked what he would like in return for his gift and the courtier surprised the king by asking for one grain of rice on the first square, two grains on the second, four grains on the third etc. The king readily agreed and asked for the rice to be brought. All went well at first, but the requirement for 2 //n// − 1 grains on the //n//th square demanded over a million grains on the 21st square, more than a trillion on the 41st and there simply was not enough rice in the whole world for the final squares. (See the **first half** of the board)

 While the number of grains on the first half of the chessboard is large, the amount on the **second half** is vastly larger. The number of grains of rice on the **first half** of the chessboard is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + ... + 2,147,483,648, for a total of 232 − 1 = 4,294,967,295 grains of rice, or about 100,000 kg of rice, with the mass of one grain of rice taken as 25 mg. his amount is about 1/1,200,000 of total rice production in India per annum (in 2005). The number of grains of rice on the **second half** of the chessboard is 232 + 233 + 234 ... + 263, for a total of 264 − 232 grains of rice (the square of the number of grains on the first half of the board plus itself). Indeed, as each square contains one grain more than the total of all the squares before it, the first square of the second half alone contains more grains than the entire first half. On the 64th square of the chessboard alone there would be 263 = 9,223,372,036,854,775,808 grains of rice, or more than two billion times as much as on the first half of the chessboard. On the entire chessboard there would be 264 − 1 = 18,446,744,073,709,551,615 grains of rice, weighing 461,168,602,000 metric tons, which would be a heap of rice larger than Mount Everest. This is around 1,000 times the global production of rice in 2010 (464,000,000 metric tons).

**The point is an exponentially growing factor have a significant impact on the growth of your idea, When you share it, others can integrate their creativity into your work, more over, more people involved, then take it from others, innovate, diversify it..... Thus your ideas, work grow** **exponentialy.**