Exponential graphs

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\(^x\).

Table of values

\(x\)	−3	−2.5	−2	−1.5	−1	−0.5	0	0.5	1	1.5	2	2.5	3
\(y\)	0.125	0.177	0.25	0.354	0.5	0.707	1	1.414	2	2.828	4	5.657	8

Detailed description

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.