1. Modeling with Excel Exponential Growth VSRI Summer 2001

2. The Model The Theoretical Solution

3. “The Recipe”

4. 1. Open new Excel Worksheet

5. 2. Enter Labels and Values for Constants in Spread Sheet ABCD 1rNodt 21.0100.01 3 4 5 Growth rate Initial Population Time Step for Recipe

6. 3. Enter Heading for Calculation Columns ABCD 1rNodt 21.0100.01 3TimeNdN 4 5 Current Time Current Population Change in Population to next Time Step

7. 4. Enter First Row of Calculations ABCD 1rNodt 21.0100.01 3TimeNdN 40=B2=$A$2*B4*$C$2 5 Time starts at 0 Equals the initial population which is stored in cell B2 r is stored in A2 absolute ref. N(t) is stored in B4 relative ref.  t is stored in C2 absolute ref.

8. 5. Enter Second Row of Calculations ABCD 1rNodt 21.0100.01 3TimeNdN 40=B2=$A$2*B4*$C$2 5=A4+$C$2=B4+C4=$A$2*B5*$C$2 New population = previous population +  population Calculate the change in population the same way as you did for the line above Next time = previous time +  t

9. 6. Copy and Paste 2 nd Row Down a “Bunch” of Rows

11. 7. Graph the Results A. Select the Time and Population Data Including the Headings

12. B. Click on the Chart Wizard. Chart Wizard

16. Going Further… Try adjusting the constant and initial population to see how it changes the population growth. Try adjusting  t to see how it changes the calculations.