MathBench > Population Dynamics

Exponential Growth and Decay

“Exponential” is not always “fast”

Before we get too much further, I want to clear up one possible misconception: the idea that an exponential growth rate is necessarily a “fast” growth rate.  The popular use of the word “exponential” suggests this, as in “the problems multiplied exponentially”.  Wow, sounds serious, and usually that’s what the speaker means. 

However, it is certainly possible to have an exponential growth rate which is quite slow.  If my bank account got 1% interest, it would still grow exponentially, just at a very slow rate! 

To see how this works, try the sliders below.  At what point is exponential growth over 10 years SLOWER than the $50 additive account?

The point is that, even with a very low rate of interest, you do always get a little more each year compared to the year before.  So, yes, its exponential, and its slow.