Kevin Matthew McKay week 2

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• week 2 assignment page

Part 1

• I tested all of the parameters at different values, but was seemingly able to find a defined carrying capacity when isolating the variable parameter "r" or net growth rate for testing
• For a very small level or "r", (1) , there was a gradual increase in cell population as time went on. No carrying capacity was reached.
• When "r" was set at 10, the population of cells seemed to stabilize at around 11. The nutrient level decreased to around 0/
• As "r" was increased, the quickness of the populations move to carrying capacity (all around 11 cells) increased. The line on the plot became steeper quicker, and then leveled out.

Tests 1-5 r values:10, 50, 100, 1000, 1

• File:Test1.fig
• File:Test2.fig
• File:Test3.fig
• File:Test4.fig
• File:Test5.fig

Part 2

• Logistic growth depends on carrying capacity, in our model, the parameter "a" can either increase or decrease the carrying capacity.
• When "a" was very small (0.01), the nutrient level stayed high and the cells died out quickly.
• It was not until a level of a=10 (a larger carrying capacity) that cells started thriving and nutrient began to dwindle
• A carrying capacity at 10,000 however, did not make much of a difference then a carrying capacity of 10, because there was not enough nutrient to support a comparably sized population of cells.

Tests 6-10 a values:0.01, 0.1, 1, 10, 10000

• File:Test6.fig
• File:Test7.fig
• File:Test8.fig
• File:Test9.fig
• File:Test10.fig