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Exponential Growth and Decay Tea

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					Exponential Growth & Decay                                                       Teacher Notes
                                              M & M Lab
I. Placement in Curriculum: This lab may be used in College Review Math, Algebra II,
   Analytic Geometrym, and Analysis of Functions classes. It can be completed in one class
   period.
II. Preparation of Materials
       A. You will need a small (bathroom sized) cup, with 40 to 50 M&M’s, for each group of
          students. Students will also need a large paper towel or napkin on which to pour the
          M&M’s.
       B. Each student should have a copy of the worksheet, a pencil and a graphing calculator.
III.      Activity
       A. Students work in pairs. (One group of 3 may be necessary.) Caution them to wait until the
          activity is complete, before eating the M&M’s. Also point out that it is difficult to see the
          “m” on the yellow M&M’s.
       B. Students work on the exponential growth side of the worksheet first, following the
          directions on the sheet.
       C. After completing the exponential growth activity, they work on the exponential decay
          activity, again, following the directions on the worksheet.
       D. Usually, at least one group will run out of M&M’s before completing the last trial. They
          will try to enter the data, and will find that the calculator is reading “error”. This is
          caused by entering the value of 0 in the list showing the number of M&M’s for each trial.
          Hopefully, they can be lead to discover where the error lies. (The calculator is not broken.
          J The exponential function has a horizontal asymptote at y = 0. Since the graph never
          crosses the y-axis, there can be no y value of 0. )
Exponential Growth & Decay #_____                          Name____________________
                                                           Date_______________Per.__
                             m
Growth                                                                           m
                       m         Don’t eat the M&M’s yet.
1. Gather the data.                                                     m
                                                                                       m
   a. Start with 4 M&M’s in the cup.
   b. Shake the cup and pour the M&M’s onto the paper towel. Count the number of M&M’s
      that have the M showing. (Be careful with the yellow M&M’s. It is hard to see the M.)
   c. Add a new M&M for each one with an M showing. Record the total number of M&M’s in
      the table below. (Trial #1 is the starting 4, continue with #2.)
   d. Repeat Steps b & c, recording the new total each time, until there are 7 trials on the table.
2. Graph the data: Create a scatterplot of Trials (x) and Total Number (y)
          Trial #   Number
             1        4
             2
             3
             4
             5
             6
             7



3. Find the formula: (Use Graphing Calculator.)
   a. Clear lists. (2nd, MEM, 4, ENTER)
   b. Enter data. (STAT, 1, and enter the data)
   c. Find a and b of y = abx .(STAT, CALC, ExpReg, ENTER, ENTER)
   d. Use Y= screen to enter the equation using the a and b values found in the previous step.
   e. Set Window. (-.4, 18.4, 1, -6, 366, 1, 1)
   f. Look at graph.
4. Questions:
   a. Write the exponential equation for this data:
   b. Predict the number of M&M’s on Trial #9:
   c. Predict the number of trials needed to have 300 M&M’s:
   d. Explain the meaning of a and b in the equation:
   e. Suppose you made the beginning number (4) Trial #0. How would your graph have
      changed?
   f. How would the equation have changed?

                                 Don’t eat the M&M’s yet.
                           Continue on the back of the worksheet.
Growth & Decay Lab                                                                 Page 2
Decay
                                             Not yet.
5. Gather the data.
   a. Start with a cupful of M&M’s. Shake the cup and pour the M&M’s onto the paper towel.
      Count the total number of M&M’s and write that number on the table below, for Trial #1.
   b. Remove all the M&M’s that have the M showing. Record the number of M&M’s
      remaining for Trial #2. Return the remaining M&M’s to the cup. Shake the cup and pour
      the M&M’s onto the paper towel.
   c. Repeat Step b, until the table is filled in.
6. Graph the data: Create a scatterplot of Trials (x) and Number (y)
          Trial #   Number
             1
             2
             3
             4
             5
             6
             7




7. Find the formula.
   (Follow directions on page 1)
8. Questions:
   a. Write the exponential equation for this data:
   b. Predict the number of M&M’s on Trial #8:
   c. Predict the trial when you would run out of M&M’s:
   d. Use the equation to predict the number of M&M’s in Trial # -1 (2 times before Trial #1)    :

   g. Use the equation to predict the trial when there would be 900 M&M’s (a negative number):

   h. Explain the meaning of a and b in the equation:


     m
             m
                        JYou can eat the M&M’s now.J                                     m

                                                      m                  m