Exponential Growth

Good news everybody!  My bank account is growing exponentially!  Of course, the bank is only paying me about 2 bucks in interest every year.  And today we're going to have a lesson on how those are not contradictory statements.

Exponential Growth is when the growth rate depends on how much you have.  Bank accounts are generally like this.  If you have a lot of money in the bank, you get a lot of interest.  Population growth is generally like this.  Texas has a of people, and so they have a lot of babies.  North Dakota has a lot few people, so they have a lot fewer babies.  Over time, we would expect the population of Texas to get bigger and bigger in comparison to North Dakota.  In some instances where time is in discrete and equal intervals, exponential growth can also be called geometric growth.  This would apply to some contrived board game sort of situation, where each turn you get, oh, let's say, 1 sheep for each 10 sheep you have in your flock.  (I'm inventing a sheep ranching game.)

Note that the term 'exponential growth' doesn't say anything specific about the growth rate (how fast something is currently growing).  In my original example, my bank pays me some tiny amount of interest.  My money will double if I leave it in there long enough.  Unfortunately for me, this time period is probably something like 400 years.  But it will continue to double every 400 years.  If I could become immortal, I could be rich!  Very often, I find that people use exponential growth to mean that something is growing very fast.  This is often the case.  India is adding millions of people a year.  A pile of cells in a petri dish probably add millions to their number in a few minutes or hours.  Sadly, my bank account doesn't add millions of anything per year.

What other types of growth are there?  Well, linear or arithmetic growth would be where your bank gives you $100 bucks every year, regardless of how much you have in there.  This would be a huge bonus for my bank account.  Not so much for Warren Buffet's.  Alternatively, you could have polynomial growth, which would follow a polynomial (something like x^2 where something would grow 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 . . .).  Exponential growth will always win out over polynomial growth in the long run, though in some cases, like my savings account, you'd be better off to take polynomial growth, were it an option, than waiting 400 years.  I'm unlikely to live that long. :(

So, when you feel tempted to sound smart by saying that something is growing exponentially (which it very likely is), you can sound even smarter by simply saying that it is growing very quickly, which is probably what you really want to say.