Introduction to Exponential Functions: Activity Bank
Algebra 2 Honors
Name:
Class/Period:_________Date:
Paper Folding: Introduction to Exponential Functions
In this activity you will observe and record the relationship between the number of folds and number of
sheets thick of paper.
Procedure:
1. Take a sheet of paper. Fold the paper in half once. How many sheets thick is your stack? Record
the data in the table below.
2. Using the same sheet of paper, repeat the process as many times as possible. Record your answer
in the table for each trial.
Number of Folds (x)
0
Number of Sheets
Thick (y)
1
1
2
2
4
3
8
4
16
5
32
6
64
x
2x
Analysis Questions:
1. Describe how the number of sheets thick changes as the number of folds increases.
*Try to find a pattern. What is the change in y with each value of x?
2. Write an equation that describes the relationship between the number of folds and the number of
sheets thick.
*Can we write an equation to represent the data for all values of x? Work in partners for 10 minutes.
*Class discussion: teacher will plot the points from the table on Desmos. The teacher will then graph
each equation that students suggest on the same graph. Students will be able to visualize why y=2 x is
the only equation that passes through each point. Therefore, this equation must represent the
function of paper folding.
*Ask students: What exactly does this equation tell us?  You can tell the number of sheets thick by
solving 2(# folds)
3. How thick do you think the stack of paper would be if we could fold it 50 times?
Prediction (include units): ________________________________
What are some things that we need to know to figure it out?
*y=250=1.125x1015 sheets thick. But how tall is that exactly? Compare to this stack of printer paper.
4. If your paper is 128 sheets thick, how many times did you fold the paper?
*Plug 128 in for y and solve for x (number of folds): x=7 folds
5. Graph and describe the behavior of your data.
a. Include: Title, Labeled Axes (with your variables) *Number of Folds vs. Sheets Thick
b. What are your dependent/independent variables? Why?
*Dependent (x): # Sheets thick, Independent (y): # folds  the # of sheets thick depends on
how many folds.
c. Appropriate Scale (should fit the page…i.e. not too small/big) *Which quadrant is our graph
in? Why?