Exponential Paper Folding Activity

# of folds for a sheet of construction paper / Total thickness
(cm)
0 / .06 cm
1 / .12 cm
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Part 1:After watching the paper folding to the moon clip, consider two different sheets of paper and fill out the table for the two different types of paper:

# of folds for an average sheet of paper / Total thickness (cm)
0 / 0.005 cm
1 / .010 cm
2
3
4
5
6
7
8
9
10
11
12
13
14
15
  • Write an equation for the two different types of paper in the form , where a is the initial thickness of the paper and b would be the amount the thickness increases by each time (hint: it doubles).

Regular sheet of paper: a: ______Construction paper: a: ______

b: ______b: ______

equation: y = ______equation: y = ______

  • Using your two equations, determine how thick the paper would be after the following number of folds (hint, plug in the number of folds for x):

Regular sheet of paper: Construction Paper:

20 folds: ______20 folds: ______

25 folds: ______25 folds: ______

30 folds: ______30 folds: ______

  • How many folds of each type of paper would it take to get to the following locations from NCHS?

Regular sheet of paper: Construction Paper:

Disney World (470 Miles = 75,639,168 cm): ______Disney World: ______

Georgia Aquarium (26 Miles = 4,184,284.4 cm): ______Georgia Aquarium: ______

Part 2:According to the Mythbusters clip, how many times can you actually fold a piece of paper in half? ______

Number of Folds / Number of Sections
0
1
2
3
4
5
6
7
8
  1. Fold an 8.5” x 11” sheet of paper in half and determine the number of sections the paper has after each fold.
  2. Record your data in the table below and continue folding in half until it becomes too hard to fold the paper.
  3. Then make a scatter plot of your data.


  1. Determine the mathematical model that represents this data of the form , where a is the initial number of sections of the paper and b would be how the number of sections changed with each fold.

y = ______

  1. Explain in words what the mathematical model means.
  1. What might be different if you tried this experiment with wax paper or tissue paper?
  1. Using your equation, determine the number of sections given the following number of folds:
  2. 12 folds: ______
  1. 20 folds: ______
  1. 100 folds: ______
  1. This equation is an example of exponential growth. Explain why this equation would represent growth.

Part 3:Area of Smallest Section

1.Again, fold a piece of paper in half and determine the area of the smallest section after you have made a fold. What is the original area of the sheet of paper?

2.Record your data in the table below.

3.Then make a scatter plot of your data.

Number of Folds / Area of Smallest Section
0 / 1
1 / 1/2
2
3
4
5
6
7
8
  1. Determine the mathematical model that represents this data of the form , where a is the initial area of each section of the paper and b would be how the area changed with each fold.

y = ______

  1. Explain what each part of the mathematical model means.
  1. What would be the area of the smallest section of the piece of paper, if you were able to fold it 10 times?
  1. This equation is an example of exponential decay. Explain why this equation would represent decay. What is different about this equation from the growth equation?

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