Royce 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 2 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.
(less than 200 words)
A. To determine the ordered pairs for the given scenario, we need to consider the number of times the paper is folded and the corresponding thickness of the paper after each fold.
1st fold: The paper is folded once, which doubles its thickness. The thickness becomes 2 * 2 = 4 millimeters.
(Ordered pair: (1, 4))
2nd fold: The paper is folded for the second time, doubling its thickness again. The new thickness is 4 * 2 = 8 millimeters.
(Ordered pair: (2, 8))
3rd fold: The paper is folded for the third time, resulting in a doubling of its thickness. The new thickness is 8 * 2 = 16 millimeters.
(Ordered pair: (3, 16))
4th fold: The paper is folded for the fourth time, and the thickness doubles. The new thickness is 16 * 2 = 32 millimeters.
(Ordered pair: (4, 32))
5th fold: The paper is folded for the fifth time, doubling its thickness once again. The new thickness is 32 * 2 = 64 millimeters.
(Ordered pair: (5, 64))
6th fold: The paper is folded for the sixth time, resulting in a doubling of its thickness. The new thickness is 64 * 2 = 128 millimeters.
(Ordered pair: (6, 128))
B. Yes, this relation is a function. In a function, each input has only one corresponding output. In this scenario, each time the paper is folded, it is always doubled in thickness. Thus, for every input (the number of times the paper is folded), there is a unique output (the thickness of the paper). The ordered pairs obtained in Part A show that there is a one-to-one correspondence between the number of folds and the resulting thickness of the paper. This confirms that the relation is a function.