III.2 Malthusian Growth
Thomas Malthus (1766-1834) is generally credited with the idea that populations tend to grow exponentially. Exponential growth (or decay) occurs whenever the rate of change over time of a variable is directly proportional to the value of the variable. To see this in Mathematica, we use as the constant of proportionality.
![[Graphics:Images/nb3_gr_69.gif]](Images/nb3_gr_69.gif)
![[Graphics:Images/nb3_gr_70.gif]](Images/nb3_gr_70.gif)
We can plot several solution curves at once to see the behavior of the solutions.
![[Graphics:Images/nb3_gr_71.gif]](Images/nb3_gr_71.gif)
![[Graphics:Images/nb3_gr_72.gif]](Images/nb3_gr_72.gif)
ADVANCED III.2.1a Experiment with different and values. Give an interpretation of and in terms of population growth (e.g. birth rate and death rate).
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