Can you fold a sheet of newspaper in half 10 times? Newsprint is thin, and a sheet of it is rather large, so that should be easy, right?
Go ahead, try it with this newspaper. (Make sure everyone's read it first.)
How many folds did you make?
Let me guess eight? Maybe nine? That's the most we could manage, too.
What if you start with a bigger sheet of newspaper? You can try it, but you'll get the same result nine folds, no more. To understand why, you need to know something about exponential growth.
When you fold the paper once, the number of layers of newspaper doubles to two. Fold it again, and it doubles again, to four (2 x 2). Three folds makes it eight layers thick (2 x 2 x 2); four folds, 16 layers (2 x 2 x 2 x 2 see where this is going?). Five folds is 32. Six, 64. Seven: 128; eight: 256; nine: 512; and (whew!) ten: 1,024!
No wonder! On the tenth fold, no matter how big the sheet of paper is to begin with, you are trying to fold 512 layers to make 1,024 layers. Each time you fold, the number of layers multiplies by 2. Another way to say this is that the layers increase by a factor of 2.
As your paper-folding shows, doubling an amount will get you to large numbers quickly! Scientists use this concept of exponential growth when studying things like populations.
The global human population, for example, has experienced exponential growth over time. Since the first modern humans appeared, it took 2.5 million years to reach a population of 1 billion, around 1800. It took a mere 130 years to double the population to 2 billion in 1930. And 44 more to reach 4 billion in 1974.
Our doubling rate has slowed a bit since then. The world's population is about 6.2 billion today and isn't likely to reach the 8 billion mark (twice the 1974 population) until around 2030.
Sources: Used with permission from 'The Math Explorer: Games and Activities for Middle School Youth Groups,' created by the Exploratorium (www.exploratorium.edu), published by Key Curriculum Press. Copyright 2003 Exploratorium. Population data: studyworksonline.com