A man who lived in a wealthy kingdom had performed a great deed.  When the King learned of this he decided to reward the man and asked him what he would like as his reward.  Seeing a chessboard in the King's chamber he asked for one grain of rice to placed on the first square, 2 on the second square, 4 on the 3rd, 8 on the fourth and so on, to the last and 64th square.  The King, not fully understanding the implications of this request, said that he would gladly reward the man as he stipulated and ordered that the rice be brought in.  Things began nicely, but the amount of rice required for each square quickly became enormous. The 21st square required more than a million grains rice. The 41st square required more than a trillion grains and the ruler exhausted all the rice in all the land before he reached the 64 square.

This is an example of exponential growth.  To demonstrate this visually I have created images, with black pixels representing the grains of rice.  I stopped at the 21st square.

<br /><br />
1. Inside this red rectangle is 1 black pixel.<br />
<img src="1.png" /><br /><br />
2. Inside this red rectangle are 2 black pixels, or twice as many as the previous rectangle.<br />
<img src="2.png" /><br /><br />
3. Inside this red rectangle are 4 black pixels, or twice as many as the previous rectangle.<br />
<img src="4.png" /><br /><br />
4. Inside this red rectangle are 8 black pixels, or twice as many as the previous rectangle.<br />
<img src="8.png" /><br /><br />
5. Inside this red rectangle are 16 black pixels, or twice as many as the previous rectangle.<br />
<img src="16.png" /><br /><br />
6. Inside this red rectangle are 32 black pixels, or twice as many as the previous rectangle.<br />
<img src="32.png" /><br /><br />
7. Inside this red rectangle are 64 black pixels, or twice as many as the previous rectangle.<br />
<img src="64.png" /><br /><br />
8. Inside this red rectangle are 128 black pixels, or twice as many as the previous rectangle.<br />
<img src="128.png" /><br /><br />
9. Inside this red rectangle are 256 black pixels, or twice as many as the previous rectangle.<br />
<img src="256.png" /><br /><br />
10. Inside this red rectangle are 512 black pixels, or twice as many as the previous rectangle.<br />
<img src="512.png" /><br /><br />
11. Inside this red rectangle are 1,024 black pixels, or twice as many as the previous rectangle.<br />
<img src="1024.png" /><br /><br />
12. Inside this red rectangle are 2,048 black pixels, or twice as many as the previous rectangle.<br />
<img src="2048.png" /><br /><br />
13. Inside this red rectangle are 4,096 black pixels, or twice as many as the previous rectangle.<br />
<img src="4096.png" /><br /><br />
14. Inside this red rectangle are 8,192 black pixels, or twice as many as the previous rectangle.<br />
<img src="8192.png" /><br /><br />
15. Inside this red rectangle are 16,384 black pixels, or twice as many as the previous rectangle.<br />
<img src="16384.png" /><br /><br />
16. Inside this red rectangle are 32,768 black pixels, or twice as many as the previous rectangle.<br />
<img src="32768.png" /><br /><br />
17. Inside this red rectangle are 65,536 black pixels, or twice as many as the previous rectangle.<br />
<img src="65536.png" /><br /><br />
18. Inside this red rectangle are 131,072 black pixels, or twice as many as the previous rectangle.<br />
<img src="131072.png" /><br /><br />
19. Inside this red rectangle are 262,144 black pixels, or twice as many as the previous rectangle.<br />
<img src="262144.png" /><br /><br />
20. Inside this red rectangle are 524,288 black pixels, or twice as many as the previous rectangle.<br />
<img src="524288.png" /><br /><br />
21. Inside this red rectangle are 1,048,576 (1.04 million) black pixels, or twice as many as the previous rectangle.<br />
<img src="1048576.png" /><br /><br />