Question

George is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is doubled. The paper starts out flat, with a thickness of 1 millimeter.

A. Write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. Explain how you came up with your ordered pairs.

Answer 1

The thickness of the paper doubles each time it is folded. Starting with a thickness of 1 millimeter, the ordered pairs showing the output as the thickness of the paper when it is folded can be listed as follows: (0, 1 mm), (1, 2 mm), (2, 4 mm), (3, 8 mm), (4, 16 mm), (5, 32 mm).

Step-by-step explanation:

The thickness of the paper doubles each time it is folded. Starting with a thickness of 1 millimeter, we can create a list of six ordered pairs showing the output as the thickness of the paper when it is folded a certain number of times:

1. (0, 1 mm) - the initial thickness of the paper.
2. (1, 2 mm) - after the first fold, the thickness doubles.
3. (2, 4 mm) - after the second fold, the thickness doubles again.
4. (3, 8 mm) - after the third fold, the thickness doubles once more.
5. (4, 16 mm) - after the fourth fold, the thickness doubles again.
6. (5, 32 mm) - after the fifth fold, the thickness doubles one last time.

To obtain these ordered pairs, we simply start with an initial thickness of 1 and double it for each subsequent fold.