Introduction to Exponential Functions Activity

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					                               Introduction to Exponential Functions: Activity Bank

Activity 1: Paper Folding

Topic:                  Introducing the exponential function:           (individual activity and class discussion)

Materials Necessary:            8.5 x 11 inch sheet of paper, Handout (see attached)


    1.   Give each student a sheet of paper and a data spreadsheet
    2.   Have the students fold the paper in half once. Make sure there is a sharp crease in the paper
    3.   Have the students unfold the paper and count the number of rectangles that result.
    4.   Have the students continue the process of folding and counting the rectangle formed.
    5.   Analysis questions: (on handout with data spreadsheet)
             a. How did the number of folds in your paper affect the number of rectangles on you paper?
             b. By what numerical value does the number of rectangles change with respect to the number of
             c. Is this a linear function? Quadratic? If not, how would you describe the behavior of what is
             d. How would the problem have changed if we folded the paper in thirds? In quarters?
             e. Write an equation to model the data where…
                      i. x = number of folds
                     ii. y = number of rectangles

Activity 2: Exponential Growth/Decay Simulation: AIDS Epidemic

Topic:                          Introducing Concept of Exponential Growth and Decay (small group activity)

Materials Necessary:            Box lid (photo copy paper box lids work the best)

                                1 cup red kidney beans and 3 cups white beans


    1. Break students into groups and give them the materials (box lid, kidney and white beans)
    2. Follow the directions to the simulation on the spreadsheet (see attached sheet for details.

Activity 3: Exponential Growth and Measurement

Topic:                  Application and Extrapolation of M&M Data

Materials Needed:               Materials for AIDS simulation, replace beans with M&M’s


    1. Take data from AIDS Simulation
    2. Ask students to extrapolate from the data and predict the number of M&M’s needed to complete 100 trials
       of the experiment. (developing the model of the data and a prediction equation)
    3. To develop higher levels of understanding, have the students to determine the dimensions of a container
       that could hold such a number of candies (connections to volume, proportion, and measurement)
   Activity 4: Determining Growth Rate

   Topic:                     Application and Extrapolation with M&M’s Data

   Materials Needed:          Materials for AIDS Simulation, replace beans with M&M’s


       1. Take data from AIDS Simulation
       2. Ask students to extrapolate from the data to calculate the number of trials necessary to reach 1 million
          candies. (calculating x rather than y)
       3. Have students determine the growth rate of the M&M’s as well.
       4. Application: Cockroach Population Growth
              a. Graph the data with population as a function of time
              b. Determine an appropriate model for the function
              c. Assume that three cockroaches cover one square inch of ground and each cockroach lives for at
                  least sixty days.

Data Banks:                                           Exponential Growth: Cockroach Data

Exponential Decay Data:                                   Cockroach Covering Times
                                                     Area                      Covering Time
  Data About African
Black Rhino Population                     Floor of 20’ by 24’ Room     16 days, 15 hours, 53 minutes
                                            Land area of Brooklyn         37 days, 1 hour, 4 minutes
   Year      Population
                                             (70.61 square miles)
             (in 1000s)
                                         Land area of New York City      39 days, 5 hours, 30 minutes
  1960           100
                                              (321 square miles)
  1980            15
                                            Land Area of New York       46 days, 10 hours, 18 minutes
  1991           3.5
                                            (47,214 square miles)
  1992           2.4
                                         Land Area of United States     53 days, 15 hours, 46 minutes
                                          (3,537,438 square miles)

                                  Websites for Exponential Function Activities

Penny Simulation and Paper Folding:                  

Paper Folding:      

Spreading Rumors:            
Pre-Calculus/Trig 3                                           Name __________________

                                                              Block ________

                                     AIDS: The Preventable Epidemic
In this exploration, you will use a model to examine the spread of infectious diseases.


   1) Pour one cup of red beans in a flat box. Each red bean represents a healthy, disease-free individual.
   2) Place one white bean in the container. This bean represents an individual with an infectious
   3) Gently shake the container (you will do this for 6 trials). Replace every red bean that is within 1
      mm of the white bean with a white bean. These beans represent individuals who came into contact
      with the infectious individual and have contracted the disease.
   4) Count the number of white beans in the container. Write this number in the appropriate column of
      Table 1.
                               TABLE 1: Simulated Spread of a Disease
                            Shake Number (x)            Number of White Beans








   5) Create a scatterplot (below) of your data in Table 1.
Algebra 2/Trigonometry 1                                    Name:


                         Paper Folding: Introduction to Exponential Functions

In this activity you will observe and record the relationship between the number of folds and rectangles of a
piece of paper.


   1. Take a rectangular sheet of paper. Fold the paper in half once. How many rectangles are created?
      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            Number of

   3. Analysis Questions:

           a. Describe how the number of rectangles changes as the number of folds increases.

           b. Write an equation that describes the relationship between the number of folds and the
              number of rectangles.

           c. If your paper had 128 rectangles, how many folds did you make in the paper?

           d. Graph and describe the behavior of your data

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