EXPONENTIAL FIT

The M&M Activity

Objective: To explore the basic ideas of exponential fitting by using Microsoft Excel to perform a step by step analysis of student generated data to find the best fitting exponential curve in the form y = ae^bx.

Done the other sections of the lesson.

This is my first section.

DIRECTIONS FOR THOSE WHO HAVE DONE THE OTHER SECTIONS:

2. Take a handful of the M&Ms or Skittles and count how many there are. This is trial 0.

3. Enter in the spreadsheet in cell C5 the amount of candy you counted.

4. Pick up the candy in both hands, shake them up and drop them. Count the pieces that have the M (or S) facing upward. Eat those that do not.

5. In the spreadsheet in cell B6, enter 1 for this trial. In cell C6, place how many candies you have left after your first trial.

6. Repeat the trials until there are no candies left. In the spreadsheet, make sure to keep track of the trial number and the amount of candy left after each trial.

Note: Delete the last data point (where the amount of candy = 0). Do not use it in your analysis.

7. Use the spreadsheet, as in previous sections, to find the best-fitting curve to the M&M data.

Some EXCEL commands that may be useful are:

LN() - LN(A12) or LN(100). Finds the natural log of a cell.

SUM() - SUM(A12:A21). Finds the sum of the values in cells A12 through A21.

AVERAGE() - AVERAGE(A12:A21). Finds the average of cells A12 through A21.

EXP() - EXP(2) or EXP(A12). Finds e2 or eA12 .

ABS() - ABS(-3) or ABS(A12). Finds the absolute value of a cell.

DIRECTIONS FOR THOSE WHO HAVE NOT DONE THE OTHER LESSONS:

2. Take a handful of the M&Ms or Skittles and count how many there are. This is trial 0.

3. Enter in the spreadsheet in cell C5 the amount of candy you counted.

4. Pick up the candy in both hands, shake them up and drop them. Count the pieces that have the M (or S) facing upward. Eat those that do not.

5. In the spreadsheet in cell B6, enter 1 for this trial. In cell C6, place how many candies you have left after your first trial.

6. Repeat the trials until there are no candies left. In the spreadsheet, make sure to keep track of the trial number and the amount of candy left after each trial.

Note: Delete the last data point (where the amount of candy = 0). Do not use it in your analysis.

7. Find the natural log of each candy data point in column D.

8. In cells B23 and D23 find the sum of each list and in cells B24 and D24 find the mean. In cell D25, calculate e raised to the mean.

9. The first guess for b will be found in cell E8. Enter this first guess in cell E11. The coefficient a will be calculated automatically.

10. Using your first guess for the equation, find the predicted values for the number of candies in column F.

11. In column G find the error between the predicted values and the actual data.

12. In column H find the absolute value of the error.

13. In column J find the square of the error.

14. In cell J24 find the mean of the square error.

15. Adjust the value for b in cell E7 to find the value that gives the minimum mean square error.

16. Find the equation of the best-fitting curve.

Some EXCEL commands that may be useful are:

LN() - LN(A12) or LN(100). Finds the natural log of a cell.

SUM() - SUM(A12:A21). Finds the sum of the values in cells A12 through A21.

AVERAGE() - AVERAGE(A12:A21). Finds the average of cells A12 through A21.

EXP() - EXP(2) or EXP(A12). Finds e2 or eA12 .

ABS() - ABS(-3) or ABS(A12). Finds the absolute value of a cell.