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.
(make it sound like an eight grade girl that wants to show her work but not too much work, also make it less than 200 words)
A. Here is the 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:
(0, 2) - When the paper is not folded, it has a thickness of 2 millimeters.
(1, 4) - After the paper is folded once, the thickness doubles to 4 millimeters.
(2, 8) - With the paper folded twice, the thickness becomes 8 millimeters.
(3, 16) - Folding the paper three times increases the thickness to 16 millimeters.
(4, 32) - The paper being folded four times makes the thickness 32 millimeters.
(5, 64) - Finally, folding the paper five times results in a thickness of 64 millimeters.
To come up with these ordered pairs, I started with the initial thickness of 2 millimeters. Then, for each subsequent fold, I doubled the previous thickness. For example, when the paper is folded once, the thickness doubles from 2 to 4 millimeters. This process was repeated for each fold to determine the thickness of the paper.
B. Yes, this relation is a function. A function is a relation in which each input has a unique output. In this case, for every number of times the paper is folded (input), there is a unique thickness of the paper (output). None of the ordered pairs have the same input value but different output values. Each input value has only one corresponding output value. Therefore, the relation is a function.