Paper Folding Problem (Exponential Functions)

In summary, Britney Gallivan solved the homework equation by solving for b^x which is equivalent to 2^n. She was not able to solve for b^x when given the original thickness of the paper.
  • #1
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Homework Statement



The paper folding problem was a well-known challenge to fold paper in half more than seven or eight times, using paper of any size or shape. The task was commonly known to be impossible until April 2005, when Britney Gallivan solved it.

A sheet of letter paper is about 0.1mm thick. On the third fold it is about as thick as your fingernail. On the 7th fold it is about as thick as your notebook. If it was possible to keep folding indefinitely, how many folds would be required to end up with a thickness that surpasses the height of the CN Tower, which is 533 m?

(The answer at the back of my book said it was 23 folds but I don't know how they got to that answer)


Homework Equations



The formula for an exponential function is: y=a(b^x)

The Attempt at a Solution



Knowing the height of the CN Tower I tried plugging that into a function using my knowledge of the paper thickness.

533 = 0.0001(b^x)

I then tried to solve for (b^x)

533/0.0001 = b^x

5 530 000 = b^x

At this point I'm not sure of what to do or if I did the steps correctly.
 
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  • #2
regarding to your steps, so far so good.

now, what do you know about the meanings of the values b and x?

if you can answer that, think about what happens to the thickness each time you fold it (silly obvious question but should get your train of thoughts going).

the answer should tumble out :)
 
  • #3
I assume that 'x' must be the number of paper folds but I'm not really sure what 'b' means.
 
  • #4
lets just say the thickness of the paper is 1, so when you fold it once it becomes 2, when you fold it twice it becomes 4 and so on. Think about how you model that with b^x
 
  • #5
Would b^x be equivalent to 2^n?
Because when 2 is folded once the thickness is 2^1=2
But when you fold it twice its 2^2 = 4
 
  • #6
there you go!
 
  • #7
I tried doing 2^23 because 23 folds is the answer but instead I ended up getting 8308608 which doesn't add up...do you have another way of solving it?
 
  • #8
you need to take the original thickness of the paper into account. Also, the question just want the first fold that let's you get more than the height of the tower, doesn't need to be exact.
 
  • #9
Thanks for your help!
 

1. What is the Paper Folding Problem?

The Paper Folding Problem, also known as the Folding and Cutting Problem, is a mathematical problem that involves folding a piece of paper in half multiple times and then cutting it in a specific way to create a desired shape.

2. How is this problem related to exponential functions?

The number of folds required to create a desired shape increases exponentially with the number of cuts. This relationship can be represented by the exponential function y = 2x, where x is the number of cuts and y is the number of folds.

3. Can the Paper Folding Problem be solved using algebraic equations?

Yes, the Paper Folding Problem can be solved using algebraic equations, specifically exponential functions. These equations can determine the number of folds and cuts needed to create a specific shape.

4. What is the significance of the Paper Folding Problem?

The Paper Folding Problem is significant because it demonstrates the power of exponential growth and how it can be applied to real-world situations. It also highlights the importance of mathematical problem-solving and critical thinking skills.

5. Are there any real-world applications of the Paper Folding Problem?

Yes, the Paper Folding Problem has been used in various fields such as architecture, engineering, and even in the development of solar panels. It has also been used to study the behavior of proteins and DNA molecules, as they can also be folded and cut in specific ways.

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