How to deceive dumb people with exponential growth

It is pretty easy to deceive an outsider that the last few years have made a tremendous better profit in comparison to the previous ones.

When we experience a exponential growth we get surprised to see how the growth was tremendous in the last few samples. In fact, on average, the percent growth is the same, but what is important (mainly in political matters) is to convince another that we are experiencing glorious times.

A simple analysis of various examples show us percent growing rates almost constant. That is natural. Observe the GDP growth of a developing country, or the growth on the exportation, or the growth of a large company. Usually you will find a percent growing rate that is almost constant.

If we consider than a growing rate to be a random variable with a certain mean and variance, we might sketch the growing curve. Bellow I present some simulations where the percent growing rate was modeled as a normally distributed random variable with mean 4 and some distinct variances: 4, 6, 8, and 10. The growing curves are presented bellow:



And here another sketch, where the graphics are separated according to their variances.



Lets take one graphic as an example. It is plotted with its percent growth shown bellow, along with a moving average of the percent growth.



If you juts look at the first plot, you would conclude that after time 60 and/or 80 we got a bigger improvement. But you may look things in a different way. If you look at the second subplot, you may observe the percent growth through time. Now it is easy to see that it is almost the same through time, and the first picture is clearly deceiving.

Another way to see how deceiving our first graphic was is to plot the data in a logarithm scale, as shown right bellow:



Don't believe straight away on your eyes, or you might get deceived. Don't believe on exploding graphics jumping out of the paper, they are made to deceive you. Don't believe on millions and billions on a moth of a politician. To see the truth, you have to get your hands dirty.