Create an exponential function

Question

A standard piece of paper is .1 mm thick. Each time you fold it in half, the thickness doubles. In this problem, we will figure out how thick the stack of paper would be if we could fold the paper 50 times. Create an exponential function. f(x) = AxB^x, which models the thickness paper in millimeters, after x folds.

Calculate f(5). f(10), f(15) and f(20)

Answer 1

Ok, so let's plug in the variables to the exponential function given.   After we do that, we can solve for each of the f(X) values given.

 

1)  Let A = thickness of paper = .1 mm

2)  Let B = change to A per fold = 2 (because it doubles)

3)  Let x = number of folds

3)  So, f(x) = .1 mm x 2^x

 

Now that we have the formula, you can solve for each of the x values given:

 

a.  f(5) = .1 mm x 2^5 = .1 mm x 32 = 3.2 mm

b.  f(10) = .1 mm x 2^10 = ?

c   f(15) = ?

d   ???

 

Can you solve the rest of them by yourself?  Incidentally, it used to be thought that the maximum number of times a piece of paper could be folded in half was seven times f(7), until a junior in high school proved that wasn't true:  https://en.wikipedia.org/wiki/Britney_Gallivan

 

 

 

Answer 2

f(x) = (0.1 mm)*2^x

 

where:

• f(x) is the thickness of the paper after x folds
• 0.1 mm is the paper's thickness when unfolded (x=0)
• x is the number of folds

 

f(0) = (0.1 mm)*2⁰ = (0.1 mm)*1 = 0.1 mm

f(5) = (0.1 mm)*2⁵ = (0.1 mm)*32 = 3.2 mm

f(10) = _____

f(20) = _____

 

 

Answer 3

Since the thickness doubles with each fold you are multiplying .1 by 2 x times.

 

f(x)=(.1)2^x   

 

Now just substitute values for x.

 

If you need more help leave a comment here.