Kevin Matthew McKay week 2

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.

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.

If the yeast were producing toxic waste this could be factored in. It would affect the death rate causing an increase in deaths as the population grows bigger or consumes more nutrient. So amount of waste would be affected by population size. So rate that waste kills yeast could be subtracted off of the Malthus model (population size times rate of production of waste [depending on amount of nutrient consumed]).

We could also delve into this idea of nutrient. Do yeast depend on only one nutrient to survive? We could make the model more complicated by adding in multiple nutrients and different speeds at which these nutrients enter the chemostat and are consumed.