### Exponential functions

There is a very famous problem concerning rice, a wise old man and the Emperor of China. The old man had solved a particularly vexing problem for the Emperor who offered him a reward. The old man asked for 2 grains of rice for the first square on the chess board, 4 grains of rice for the second square, 8 grains of rice for the third square, continuing until he had rice for all of the sixty-four squares. The Emperor thought this was a trivial request until his scribes worked out how much rice the old man had requested. It would bankrupt the kingdom!

The following table shows the number of grains of rice for each of the first 10 squares only.

\(x\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

\(y = 2^x\) | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 |

This is an example of a **exponential function** and we shall investigate the graph.