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How to Graph Logistic Growth

Logistic growth models the growth of a population that is subject to some constraints. These constraints could be space, food or other resources.. Together, the constraints are called carrying capacity.

In a typical logistic growth model, population increases slowly at first, then accelerates and then slows again as the population approaches the carrying capacity. However, if the population starts off above carrying capacity, the pattern above is reversed.

The logistic growth model is given by

r = rmax(K - N/K)

where r is the growth rate at a given time, rmax is the maximum growth rate, N is the population at a given time, and K is carrying capacity.

Instructions

- 1
  Draw an x-axis (horizontal), and label it "Time".
- 2
  Make tick marks on the x-axis, corresponding to the unit of time you are using. For human populations, this could be years or decades; for species that multiply faster it could be days or even hours or minutes.
- 3
  Subtract the population at Time 1 from the carrying capacity.
- 4
  Divide the result by the carrying capacity.
- 5
  Multiply this quotient by the maximum growth rate. This is the growth rate at Time 1.
- 6
  Multiply the growth rate at time 1 by the population at time 1. This is the population at time 2.
- 7
  Repeat steps 3 through 6 until the population is at the carrying capacity.
- 8
  Plot the points. Each point will have a time (on the x-axis) and a population (on the y-axis).
- 9
  Draw a smooth graph connecting the points.

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