Answer key: Spreadsheet exercises 7-8



Answer key: Spreadsheet exercises 7-8

Spreadsheet exercise 7

1. This is exactly what your initial assumptions were for the graphs you made. Note the values you put for b and d, or for r (=b-d) in both key equations used. Thus, you would expect geometric or exponential growth under these circumstances. You’ve already tested it.

2. Think about this logically: If birth rates are less than death rates, you ought to see the population decline. If you changed b and d so that b is less than d (or r d’. Watch that population grow and grow!

10. If the population grows more quickly, it will take less time to reach its carrying capacity. In the discrete time model, increasing rates lead to a cycling around K. This basically is due to the time lag. If the growth rate, and thus the time lag, is too severe, the population will crash. In the continuous time model, this doesn’t occur, and K is simply reached more quickly.

With the spreadsheet: In the discrete model, experiment with higher values of b, without changing anything else. In the continuous time model, simply change r and see what happens.

11. If you graph the census data from the site and use the “add trendline” function, you find the growth rate is approximately linear, suggesting that while we are still growing, we are on the >K/2 side of the logistic growth curve.. You can then estimate r and K by graphing ΔNt/Nt as a function of population size (i.e. graphed against Nt)—see question 4. The values obtained are:

Intrinsic rate of growth (r) = approximately 0.031

Carrying capacity (K) = approximately 11 billion

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