ADV PRE CALC Ch 3.1 EXPONENTIAL GROWTH LAB ACTIVITY: PENNIES NAME__________________________ MATERIALS: a cup of pennies 1. Put 2 pennies in a cup. (This is trial #0) Shake the cup. Dump out the pennies. See how many heads you have. Add that number of pennies to the cup. Repeat for 11 trials. Record the data in the chart below. Trial # of pennies 0 2 1 2 3 4 5 6 7 8 9 10 11 2. Input the data into the graphing calculator L1: trial Number L2: # of pennies 3. Create a scatterplot of the data 2nd Stat Plot 1: Type: first graph in menu Xlist: L1 YList: L2 Hit Zoom 9 4. The graph is an exponential growth. Let’s find the equation using the calculator. STAT CALC 0: ExpReg ExpReg L1, L2, VARS Y-VARS enter enter enter Your screen should show an equation y = abx Where x = trial number Write the equation you see:_______________________________ Hit zoom 9 to see the graph again 5. Use this equation to check on your observations a. Trial x = 5 b. Trial x = 9 observed:_______________ model prediction:____________ observed:______________ model prediction: _____________ 6. How many pennies does your model predict for trial 13? _________________ EXPONENTIAL DECAY ACTIVITY: M&M’S NAME__________________________ MATERIALS: About 40+ M&M’s, paper cup, sheet of notebook paper 1. Count your M&M’s. Record this number as Trial #0 2. You are to dump all of your M&M’s into the cup. Gently shake and dump contents of cup onto the notebook paper. All M&M’s that land with the M showing are now to be destroyed ( um…wonder how you should accomplish this task?) Count remaining M&M’s and record this number under trial 2. Return these M&M’s to cup and repeat . Do this for 7 trials or until you have “0” left. Trial 0 Number M&M’s left 1 2 3 3.Enter the data into lists L1: trial Number 4.Create a scatterplot of the data 2nd Stat Plot 1: Type: first graph in menu Xlist: L1 YList: L2 Hit Zoom 9 4 5 6 7 L2: M&M’s 5. The graph you see is an exponential decay. Let’s let the calculator find the equation using STAT CALC 0: ExpReg ExpReg L1, L2, VARS Y-VARS enter enter enter Your screen should show an equation y = abx Where x = trial number Write the equation you see:_______________________________ Hit zoom 9 to see the graph again 6. Use this equation to check on your observations a. Trial x = 3 observed:_______________ model prediction:____________ b. Trial x = 5 observed:______________ model prediction: _____________ b. Trial x = 7 observed:______________ model prediction CLASS DATA Exponential Growth Trial # of pennies 0 1 2 3 4 5 6 7 8 9 10 11 EXPONENTIAL GROWTH EQUATION: __________________________________________________________ EXPONENTIAL DECAY Note: Once a student has a “0” entry stop tabulating class data TRIAL 0 NUMBER 1 2 3 4 5 6 M&M’S LEFT EXPONENTIAL DECAY EQUATION ________________________________________________________ 7