Logistic Models (DP IB Applications & Interpretation (AI)): Revision Note

Logistic Models

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