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Exponential growth with graphs
Many things grow, but not all things grow in the same way. There are two basic ways for something to grow: linearly, and exponentially. When something grows linearly it grows repeatedly by the same amount; when something grows exponentially it grows repeatedly by the same proportion.
These graphs illustrate the processes of the two different types of growth:
Both graphs show growth, in stages, from left to right. At each stage the amount from the previous stage is in purple, with the new growth on top in green. In both graphs the first stage of growth, from the first amount to the second amount, is the same.
The left-hand graph shows linear growth. In the first stage of growth the original amount grows half as big again (50% increase) to give the second amount. Each subsequent stage grows further by that same amount. Each new green extension of growth is the same size as the previous ones.
The right-hand graph shows exponential growth. In the first stage of growth the original amount (on the left) grows half as big again (50% increase) to give the second amount. Each subsequent stage grows by that same proportion, half as big again, (50% increase). Each new green extension of growth is larger than the previous ones.
In each stage of exponential growth the growth compounds upon itself; that is, not only does the base amount grow, but the growth grows too. Compounding is another name commonly used for exponential growth.
These graphs contrast linear and exponential growth:
Both graphs show that what is being measured increases from left to right. The higher the red line goes, the more of it there is; the steeper the slope of the red line, the faster it is growing.
Both graphs start off (at the left side) with the same amount of what is being measured (indicated by the purple line), and initially growing at the same rate (the same slope, indicated by the green line on the exponential growth graph.) As the growth continues from left to right the graph of linear growth keeps the same slope while the graph of exponential growth gets steeper and steeper and goes much higher.
When something is growing exponentially the rate of growth gets greater as the growth continues and the final amount is much greater when compared to linear growth starting from the same conditions.