Exponential and Logarithmic Functions

Exponential Functions are used to model growth of populations, interest on an investment, depreciation of cars, decay of radioactivity, and many other real-life things. Logarithmic Functions are used to measure earthquakes (Richter Scale), Acidity (pH), and Sound Intensity (decibels).

Mythbuster's Paper Folding

Is it possible to fold a sheet of paper in half more than 7 or 8 times?  Folding paper in half can be modeled using the exponential growth equation. Check out the video, check out the challenge, check out the solutions. More fun resources about this problem are found at the bottom.

Watch the video and listen for "Exponential".

See if you can solve this problem:

  • Assuming you can fold paper in half an infinite number of times….
  • And given the thickness of paper = 0.001 cm,
  • And given:
    • 100cm = 1m,
    • 1000m = 1km,
    • 2.54cm = 1 inch,
    • 12 inch = 1 foot,
    • 5280 feet = 1 mile,
  • Write an equation to model the thickness of a sheet of paper after folding it in half t number of times,
  • Identify and label each term of the equation and explain what it means,
  • Determine how many times you have to fold paper in half to:
    • Reach 4 feet tall,
    • Reach ¼ mile tall,
    • Reach to the moon from earth (384,000 km)

Need help? Scroll to see the solutions:

Sometimes just seeing the answer isn't enough. Here's a video solution of the paper folding problem to find out how many folds to reach 1/4 mile tall:

Another fun site to check out: