Often times exponential growth is plotted as a straight line on a semi-log plot. The Y-axis is logarithmic and the X-axis is linear. Here is an example:
What kinds of things grow exponentially?
Clearly exponential rates of growth are an integral part of the planning process. Different aspects of a growing population have different exponential growth rates and these need to be considered.
For instance, suppose your urban area is growing
at the rate of 5% a year. How does this translate into the
Whenever schools get crowded, freeways get jammed, airline hubs get crowded, oil gets used up, there are no more available phone numbers, the federal debt goes beyond recovery, etc, etc is an indication of poor planning and trend extrapolation.
In a nutshell: there is no reason that we should ever be surprised at the rate of resource utilization. If we simply pay attention to past history, in general, its a fairly good guide for future resource use.
Exponential Growth and Material Exhaustion:
We are in real danger of running out of certain materials due to rapid consumption. In general, it is not cost-effective to search for new sources of these materials (e.g. it costs a lot of money to dig/mine deeper into the earth). Some examples include:
|Aluminum||6.4%||2007 -- 2023||Coal||4.1%||2092 -- 2106||Cooper||4.6%||2001 -- 2020||Petroleum||3.9%||1997 -- 2017||Silver||2.7%||1989 -- 1997|
The difference between linear growth (constant number of units growth per year) vs exponential growth (constant percentage increase) is difficult to see initially, if the exponential growth rate is small.
We can use the Statistical Graphical Tool to help understand this.
Here is some data:
First we try a linear fit which will clearly be seen as bogus.
Then we will try an exponential fit with 10% growth rate to see its much better.
So in this case its obvious that the growth rate is exponential but in some other case such as the population data for California its not so obvious!