3.1 The growth model in a spreadsheet

Before you begin, be sure to check the following settings (same as first asignment):

  • Open a Microsoft Excel worksheet or a Google sheet
  • Check whether the spreadsheet uses a ‘decimal-comma’ (\(0,05\)) or ‘decimal-point’ (\(0.05\)) notation.
    • The numbers given in the assignments of this course all use a ‘decimal-point’ notation.
  • Check if the $ symbol fixes rows and columns when it used in a formula in your preferred spreadsheet program.
    • This is the default setting in Microsoft Excel and Google Sheets. If you use one of those programs you are all set.

To build it repeat some of the steps you performed in assignment 2 on a new worksheet.

  • Define the appropriate constants (\(r\) in A5, \(L_0\) in A6) and prepare the necessary things you need for building an iterative process.
  • In particular, add the other parameter that appears in Van Geert???s model:
    • Type \(K\) in cell A7. This is the carrying capacity. It receives the value \(1\) in cell B7.
  • Start with the following values:
    • \(r = 1.2\)
    • \(L_0 = 0.01\)

Take good notice of what is constant (parameters \(r\) and \(K\)), for which the $ must be used, and what must change on every iterative step (variable \(L_t\)). Take about \(100\) steps.

  • Create the graphs
  • You can start playing with the values for the parameters and the initial values in cells B5, B6 and B7. To study this model???s behavior, be sure to try the following growth parameters:
    • \(r = 1.2\)
    • \(r = 2.2\)
    • \(r = 2.5\)
    • \(r = 2.7\)
    • \(r = 2.9\)
  • For the carrying capacity \(K\) (cell B7) you can try the following values:
    • \(K = 1.5\)
    • \(K = 0.5\). (Leave \(r = 2.9\). Mind the value on the vertical axis!)
  • Changes in the values of \(K\) have an effect on the height of the graph. The pattern itself also changes a bit. Can you explain why this is so?