How many times can you fold a piece of paper in half?

Today grade 11s were working on modelling exponential growth and decay. We folded paper in half repeatedly and modelled the number of sections that we get after more and more folds.

We decided this was exponential growth and the equation is y=2^x

We also looked at the page area, and how that changes as we folded more and more. Some called the initial page area 1 (measuring with a “page” as a non standard unit of measure), and then we saw that the area of each folded section decreased each time (the base is 1/2). The exponential decrease function is y=(1/2)^x. Others who measured the page and had the area in cm^2 then would have that as their “a” value for their equation.

Tomorrow we will be working on modelling word problems, so this is a good introduction to those skills.

PS. We had papers folded 7 or 8 times before it got to be too challenging to fold any further. We tried with larger pages too without any luck. Here’s a group that managed to use toilet paper and fold it 13 times.