What are the parameters of logistic models?
- A logistic model is of the form
- The L represents the limiting capacity
- This is the value that the model tends to as x gets large
- The C (along with the L) helps to determine the initial value of the model
- The initial value is given by
- Once L has been determined you can then determine C
- The k determines the rate of increase of the model
What can be modelled using a logistic model?
- A logistic model can be used when the variable initially increases exponentially and then tends towards a limit
- H(t) is the height of a giraffe t weeks after birth
- P(t) is the number of bacteria on an apple t seconds after removing from protective packaging
- P(t) is the population of rabbits in a woodlands area t weeks after releasing an initial amount into the area
What are possible limitations of a logistic model?
- A logistic graph is bounded by the limit L
- However in real-life the variable might be unbounded
- For example: the cumulative total number of births in a town over time
- A logistic graph is always increasing
- However in real-life there could be periods where the variable decreased or fluctuates
The number of fish in a lake, , can be modelled by the function
where is the number of months after fish were introduced to the lake.
Initially, 50 fish were introduced to the lake. Find the value of .
Write down the limiting capacity for the number of fish in the lake.
Calculate the number of months it takes until there are 500 fish in the lake.