3-3 Equation Play

Playing With the Population Equation

This is a perfect job for a computer or a scientific calculator which doesn’t mind doing simple calculations over and over again. If you have a computer available or a TI82 or above that has a spreadsheet program, you can write an equation which will automatically produce graphs for different growth rates and different starting populations.

We’ve worked out two examples in this chart. In both examples we start with a normalized population of .1 (10% of the carrying capacity), and calculate the normalized population each year for a total of twenty years. Example 1 assumes a population growth factor of 2.0. Example 2 assumes a population growth rate of 3.0. Since these numbers represent the normalized population, they might represent hundreds, thousands, or even millions of individual goats, rabbits, or insects. Graph the two examples.

Compare the graphs. Describe how the populations which grow at these two different rates change over time. How do they apply to the population of goats on Goat Island?

Year Population 1 Population 2
n 2.0 pn (1-pn) 3.0 pn (1-pn)
1 0.100 0.100
2 0.180 0.270
3 0.295 0.591
4 0.416 0.715
5 0.486 0.598
6 0.496 0.721
7 0.499 0.603
8 0.500 0.718
9 0.500 0.607
10 0.500 0.715
11 0.500 0.611
12 0.500 0.713
13 0.500 0.614
14 0.500 0.711
15 0.500 0.616
16 0.500 0.709
17 0.500 0.618
18 0.500 0.708
19 0.500 0.620
20 0.500 0.707

 



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