If you go to www.npq.org, you'll find the table I've been using for my data.  THEY predict that the world's population in 2050 will only be 9,309,051,539!

That's WAY off our guess.  Why were we so far off?

Well, remember the graph
of exponential growth?
graph of exponential growth

It turns out that, in the long run, populations don't really grow exponentially.  Because of other factors like disease, war and limited resources, population growth starts to slow down.

graph of logistic growth This is called logistic growth.

(And it's got a really messy

But, lucky for us, exponential growth and our formula is a great short-term predictor (model) for populations.  It just doesn't work well for large time spans.


If there are 25,329 alien bacteria in your petrie dish at 6am and 100,000 at 7pm, find the rate of growth.

*Note that this is bacteria -- not alien amoebas!

Use this rate to predict how many alien bacteria there will be at midnight.