Learn about exponential growth in this experiment so that you can fold paper to the moon!
It doesn’t take as many folds as you think!
Materials:
Paper and a calculator
Time Estimated:
5 min
Directions:
Take a piece of paper and fold it in half. How many layers is it? (2)
Fold it in half again. How many layers is it now? (4)
Fold it in half again. How many layers now? (8)
What do you expect to happen if you fold it in half a fourth time? (16 layers)
Can you identify the pattern? (if n is the number of times you folded, the pattern is 2^n, or 2 x 2 x 2 x 2 x… n times)
A piece of paper is about 0.1 mm thick. Using the pattern you came up with previously, can you figure out how thick the stack is after 2 folds? After 3 folds? After 10 folds? (use 0.1 x 2^n) (answers: 0.2 mm, 0.4 mm, and 102.4 mm)
What is the thickness after 42 folds? The distance between the earth and the moon is around 384,400 kilometers (remember 1 km = 1,000,000 mm). After 42 folds, would the paper reach the moon? (439,804,651,110.4 mm = 439,804.7 km, so yes, it would reach the moon because 439,804.7 > 384,400)
Think Like A Scientist:
How many times can you actually, physically fold the paper?
Is it possible to fold it 42 times? What stops you from being able to fold it this many times?
Is there any way to fix this problem so that you could fold the paper more times?
How It Works:
In this experiment, you learned about exponential growth! This type of growth is called exponential because the equation to model this is 2^n, which is some number (in this case the number 2) raised to an exponent (n). Exponential growth can start small, but then will get big very very quickly! In this example, with each fold, you double the layers of paper you had in the previous fold. In other words, you multiply the layers by 2 each time you fold. This graph gives a visual representation of how fast the thickness of the paper grows.
First, notice that along the vertical axis, every line represents 50,000 km. Given that our paper starts at 0.1 mm = 0.0000001 km, you can’t really see the increase in thickness for folds 1-35 on this graph. However, once you get to 36 folds we can notice the increase, and then it grows very fast! We can see this because the line suddenly curves up very steeply, and by 43 folds it is almost at 450,000 km!
Looking for more fun at home STEM activities for your young scientist? Check out our workbook full of exciting science experiments and empowering activities!
