The values of y = 2\(^x\) for a number of values of x were obtained using a calculator, and are shown in the table below.
We can then plot the ordered pairs (x, 2\(^x\)) to produce a graph of y = 2\(^x\).
Note that although we have 'joined the dots' to form a smooth curve, we have not given any meaning at this stage to 2\(^x\) when it is an irrational number; thus we cannot deal with this problem at this stage.
We note the following features of the graph:
- The graph is increasing.
- The values increase quite rapidly as we move along the axis.
- On the left-hand side, the graph approaches, but never reaches, the axis.
How much rice?
The old man had requested 36 893 488 147 419 103 230 grains of rice.