watching things grow - reading numbers

Strangely I often see data representing long term growth represented linearly. Personally I think this is good for 'dramtics' but I don't think it really gives a clear view of what's happening over time.

So I thought I'd toss in a few thoughts on that topic while I wait for an SCP to complete....

Assuming we start with 1 and add 1 to it we get a linear growth of 1, 2,  3, 4 ... which we see below in the figure. I've put in two columns where growth is adding 1 each time and the other where growth is adding 10% each time. When you have 1 adding 1 is really doubling your holdings, but adding 10% isn't.

But when you've got 20 adding 1 is only adding 1 and not really much. I mean seriously if you were out on the town and had twenty bucks adding another buck won't buy you much more.

So 'linear growth' starts to be tricky to comprehend when you get a few cycles into the analysis. In the plot above I've only looked at 30 cycles of of 'activity' and already on the log plot the line of 'linear growth' is seeming to show that reducing importance of giving you a buck when you've got thirty already. The Log plot is however showing a more 'linear' view of your growth ... which is of course because our growth is done in percentages ... which is what a logarithm is all about.

This 'aspect' can be seen clearly when we look over a longer time scale, and adding a buck to what you have makes bugger all difference (but adding 10% is still adding 10%).
 

So this is why financial analysis should make better use of maths tools to express issues. Assmuming the idea is to communicate something rather than obsfucate something