High School

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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. (5 points)

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

Answer :

Answer:

See below.

Step-by-step explanation:

Let x represent the number of folds, and y represent the thickness.

So, the first ordered pair is:

(x,y) = (0,1)

When x increases by 1, the value of y gets doubled.

So, the six ordered pairs are:

[(0,1),(1,2),(2,4),(3,8),(4,16),(5,32)]

Is it a function?

Yes.

-hope it helps

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Rewritten by : Barada

Final answer:

A list of six ordered pairs representing the paper's thickness as it is folded shows a function, with each input having exactly one output, starting from 1 millimeter and doubling with each fold.

Explanation:

Part A of the question asks for a list of six ordered pairs representing the thickness of a piece of paper as a function of the number of times it is folded. The initial thickness is 1 millimeter, and it doubles with each fold. The pattern follows a geometric sequence where each term is twice the previous term. The first fold results in a thickness of 2 millimeters (1mm doubled), the second fold results in 4 millimeters (2mm doubled), and so on. The list of ordered pairs would therefore be:


  • (0, 1)

  • (1, 2)

  • (2, 4)

  • (3, 8)

  • (4, 16)

  • (5, 32)

Part B identifies this relationship as a function because for each input (number of folds), there is exactly one output (thickness of the paper). No input corresponds to more than one output, thus satisfying the definition of a function.