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. B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A.
The input value is the number of times you fold it. The input value is also known as the x-value. The output value is its thickness. The output value is the y-value. When you don't fold it all, the thickness will remain the same, which is 1. The ordered pair would be (0,1). When you fold it once, the thickness will double from 1 to 2. The ordered pair would be (1,2). When you fold it a second time, the thickness will double from 2 to 4. The ordered pair would be (2,4). Fold it one more time, and the thickness will be 8. The ordered pair is (3,8) Fold it the fourth time, and the thickness doubles. 8 x 2 = 16. The ordered pair is (4,16) Fold it the fifth time, and the thickness goes from 16 to 32. The ordered pair is (5,32) The ordered pairs would be: (0,1) (1,2) (2,4) (3,8) (4,16) (5,32) (6,64) (7,128) and so on :P The question asks for 6 ordered pairs, so I bolded the first six. Now, the equation for this would be [latex]y = 2^x[/latex] If we graph that, and we do the vertical line test, then we know this is a function. It is a function because each x-value has a different y-value. There are no y-values that have the same x-values. I have attached the graph of that line.