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I've always heard Stock investment being described in terms of getting X% return per-year in the long-running. But looking at the FTSE in the long-term doesn't suggest an exponential growth? See below, clipped from Google.
It's remarkably linear, with deviations for the various bubbles and crashes, but returning to a linear base-line value.
What gives?
The main problem is that indexes like the FTSE only show growth in share price. The FTSE 100 is, by definition large companies, and most of those would be regarded as dividend rather than growth stocks.
You need to look at a total return index to get a more accurate picture because if you reinvested dividends you would see an additional ~4% compound growth over 30 years.
https://www.schroders.com/en/insights/economics/how-the-ftse-100-returned-94-without-moving/
Part of the reason you're seeing this trend is that you're looking at a particularly interesting time in the history of the stock market. It includes the September 11th market drop which in turn led to the Great Recession. The period from somewhere around 2000 - 2012 is considered "The Lost Decade." Essentially that means that stock prices went from where they were at the start of the decade, down into a nosedive in a severe bear market, and then back up to where they started over the course of about a decade. If you had invested a lump sum in 2000, then went to take a look at it in 2012, you'd see that you had almost the exact same amount of money as when you started, give or take a very small percentage.
I found this nifty article on the time period (and on why dollar cost averaging is almost always the way to go when investing in a portfolio) that can shed a little bit more light. To the best of my knowledge, the last time the Stock Market did anything remotely similar was the Great Depression. As has also been mentioned-- you're looking at just dividend stocks instead of growth stocks, and about 1/3 of the times period you're evaluating is during a recession, while another 1/3 is during one of the longest economic booms in the history of the stock market.
Stock and bond indexes, or stock and bond funds, or individual stocks and bonds don't show linear growth, or exponential growth. Depending on the time period they can show growth or decay. Those types of change in a specific time period can appear linear, exponential, logarithmic...
Investments can't show a consistent pattern because the change in prices and value is based not on time, but on sales, estimates sales, perception of hotness of those sales. It can also be based on rumors that can drive the price up or down. Just look at how the markets react to the guess on how a vote will go. Those prices of individual stocks can also be moved by market and industry beyond their control.
Look at your chart, it is easy to find periods of up to 10 years where the growth was zero or even negative. Of course your chart ignores that most people don't buy all their investments on one day and then let it ride for a few decades. My retirement fund started with a initial 401(k) contribution of ~$100 that was matched by ~$50 from my employer.
