Under normal circumstances, animal populations grow continuously.

So, here's the formula for population growth (which also applies to people).  I'm just going to change the letters a little:


The P (sub o)  is pronounced "P not."
The little "o" is a zero for time =
0... when you start.

* time is usually in hours or years

Let's just do one -- they're really easy!

In 1950, the world's population was 2,555,982,611.  With a growth rate of approximately 1.68%, what was the population in 1955?

First, let's figure out what everything is:

06-exponentials-02.gif 06-exponentials-03.gif


Let's ignore the decimal part since it's not a full person.

So, our guess is that the world's population in 1955 was 2,779,960,539.

(The actual population was 2,780,296,616 so we were pretty close.)

We'll be doing more with populations after I've taught you some more stuff.


At 5pm, you count 26,300 alien bacteria in your petrie dish.  If the growth rate is 2.7%, how many bacteria will there be at midnight?