Paper Folding Problem (Exponential Functions)

[psav5]

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.

 

[wukunlin]

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 :)

 

[psav5]

I assume that 'x' must be the number of paper folds but I'm not really sure what 'b' means.

 

[wukunlin]

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

 

[psav5]

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

 

[wukunlin]

there you go!

 

[psav5]

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?

 

[wukunlin]

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.

 

[psav5]

Thanks for your help!