Graham 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 3 millimeters.
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.
B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A. (5 points)
A. The ordered pairs can be found by doubling the thickness of the paper each time it is folded. Starting with a thickness of 3 millimeters, the ordered pairs would be as follows:
(0, 3) - The initial thickness of the paper before any folds.
(1, 6) - The thickness after the first fold (2 * 3 = 6).
(2, 12) - The thickness after the second fold (2 * 6 = 12).
(3, 24) - The thickness after the third fold (2 * 12 = 24).
(4, 48) - The thickness after the fourth fold (2 * 24 = 48).
(5, 96) - The thickness after the fifth fold (2 * 48 = 96).
B. Yes, this relation is a function. In a function, each input (number of times folded) corresponds to exactly one output (thickness of paper). As seen in the ordered pairs above, there is only one thickness value for each folding value, which fulfills the requirements of a function.