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The purpose of this blog is to help you improve your productivity and efficiency. The upside of that is that you will see growth in various aspects of your life. It might be that your knowledge of a particular area improves, or your free time or annual salary increases – everything grows when we try and improve it.

One assumption that we often make is that things will grow linearly, and we get frustrated when they don’t. The reality is that there are 2 main growth trends.

Growth Type 1 – Exponential Growth

Using an arbitrary example of project completion, the chart below shows a typical exponential growth curve (with the noise removed)


The above project gets off to a slow start. This is usual where you need to get up to speed with a particular method, or a new subject. Once you do pick it up though, you rapidly pick up the pace, and with the above example, 95% of the project is completed in the final 50% of the allotted time.

Another situation where this is applicable is with website growth. As I write this article (February 2013), it is only the third article on the site. The site has only just been indexed by Google and is starting to appear in the search records. Traffic is very low. It will stay low for quite some time too. But as the traffic increases, word of mouth will increase. Think of it this way, for each person that sees the site, they will tell 5 of their friends. These 5 friends then check out the site and 3 of them tell 5 of their friends, and so on. You can soon see how word of mouth can be exponential.

Other examples of situations that would grow exponentially are:

  • Traffic to a website
  • Wealth
  • Business growth
  • Moore’s Law

Growth Type 2 – Logarithmic Growth

Logarithmic growth follows the opposite trend to exponential growth.


Here I am using the example of productivity. When looking at implementing new productivity methods (in the above example using the number of reports released per week as a measure), there will often be a fast increase in productivity, which then plateaus out as you reach the limitations of that particular method.

Another example would be athletic performance. A novice athlete would be able to shave seconds and even minutes off their performance with minor changes to their technique and through practice. However, when you get up to Olympic level, improvements would tend to be measured in milliseconds. So, the above graph could equally represent a graph of run times throughout a year of training (all be it inverted – you’d be very disappointed if your run time increased with training!).

Other examples of logarithmic growth include:

  • Athletic performance
  • Learning a new technical skill
  • Sales of a product following a big pre-launch campaign – e.g. movie sales
  • Weight gain / loss
  • Productivity and efficiency

Third type of Growth

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After saying earlier that there are two main types of growth, there is a third. Essentially it is a combination of exponential and logarithmic. Basically, growth starts off slow and then builds up momentum. After a period of rapid growth however, further improvement tends to tail off.

One example of this would be the growth of a website targeting a particular market. As mentioned before, as a website gets off the ground, it grows exponentially. However, if the website sticks within its own market, and if the market is not growing in parallel, eventually the growth will reach a saturation point, where they have attracted the majority of the market.

Another example would be in project management. This type of curve is commonly referred to as an “S-curve”. As an example, a wing assembly is being designed and sizes calculated. As the project gets off the ground, stress analysts are still finding their feet with the analysis methods required, how the structure is loaded etc. The first few reports are slow to be completed, but then as the analysts become more comfortable with the approach, momentum builds and growth speeds up. However, as the project reaches the end, this tends to be where the difficult analyses end up being completed, as they may have been started earlier on, but due to difficulties achieving a good result, they are still on-going and so growth decelerates toward the end.

Frustrations associated with Growth

The most common frustration associated with growth is usually based on the initial assumption of a linear growth model. This results in one of 2 things:

i) Frustration and eventually quitting, because growth isn’t fast enough. Assuming a linear model will result in very slow growth based on initial numbers. Areas subject to exponential growth are full of quitters. The key message – don’t give up!


ii) If growth is actually logarithmic, and a linear assumption is assumed, then final results will be over-estimated. This often happens with business start-ups. If you have ever watched Dragons Den, the Dragons are quick to pounce on unrealistic growth models, where the entrepreneur is forecasting sales totalling millions of pounds within 4 years. Alternatively, a much earlier finish to the project is anticipated, which results in a very dim view of project management.


How to cope with these frustrations

The first and most important step is to predict what type of growth you are expecting. Look at other situations similar to yours and look how that grew. For instance, when learning, look at the distribution of beginners, amateurs and experts. This will indicate the drop off rate and thus at what stage continued growth tends to slow down.

A friend of mine has a huge desire to learn. However, she gets incredibly frustrated when the learning is slow. Mainly because she expects the learning process to continue at the same rate. This would be avoidable if she hadn’t assumed a linear growth model.

Once you have assessed the growth model to expect, it becomes easier to accept any deviations. With exponential growth, you accept that there will be a long “bed-in” period while traction grows.

With logarithmic growth, you are also prepared for the plateau as business slows down. With that in mind, you might put a plan into place to branch out into a new market, so as one particular part of your business slows, another grows – and thus your overall business continues to grow.

So, with that in mind, what areas have you seen the different types of growth in and what other types of growth have you noticed? Please leave a note in the comments.