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The logistic growth model

1. Graphical represenation of the relationships

time series of population, growth rate changes with population

sketch of how this could be related to resources

	growth rate is faster when more resources are available there is a maxium growth rate
	resources left over and population are inversely related when all the resources have been consumed, the population stops growing
	the growth rate starts out at a maximum, with high resources and decreases to zero when resources run out

 

2. equation to describe this is:

growth_rate = growth_rate_max * (K - N)/K

or

y	=	m	*X	+B
growth_rate	=	(- growth_rate_max/K)	*N	+ growth_rate_max

 

3. Calculating the change in population growth_rate * population = change_in_population

this is interesting because the growth_rate depends on the population

as the population grows the growth rate will slow down

at any population size = N

growth_rate = growth_rate_max*(K - N)/K

example: growth_rate_max = 0.1 month^-1

K = 1000 rabbits

population = 500 rabbits

growth_rate = 0.1 * (1000-500)/1000 = 0.05 month^-1

change in population per month =

0.05 month ^-1 * 500 rabbits = 25 rabbits per month