In my new book Brain Gain: Technology and the Quest for Digital Wisdom, I used an example (on page 242) that did not accurately portray the distinction I was trying to make. Rather than a linear, arithmetic sequence, I used a low-rate (10 percent) compounded sequence (which will double in a fixed time period as well, although much more slowly.)
A much better example, that I should have used, would be the following:
“For example, if you start with $100 and it grows at a linear, non-compounded rate, of say $100 dollars per year, you will get the following kind of growth:
100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 1,100, 1,200, 1,300, 1,400, 1,500…
Not bad—in 15 years your money has gone up substantially.
But if, instead, that same $100 grows at an exponential rate, doubling every year, (which can be easily calculated, for those interested, as 2 to the “number of doublings” power) you get:
100, 200, 400, 800, 1600, 3200, 6400, 12800, 25600, 51200, 102400, 204800,
409600, 819200, 1,638,400…
In only 15 doublings you are not at $1,500 but over $1 million (just a slight difference!).”
Many thanks to Seb Schmoller for pointing this out!