10: A test for exponential growth

Actually, its very useful that only exponential growth gets straightened out by log transformation. Now we have a quick-and-easy test to find out if a population is undergoing expontial growth. Namely

  1. Plot the population on log paper.
  2. Decide if the trajectory forms a straight line.

That’s pretty much it!! A straight line on graph paper means exponential growth (if the line goes up) or exponential shrinkage / death (if the line goes down). If the line is straight but completely flat, it means no change, just like on a regular graph.

So, looking at the graph below…

When was the population growing exponentially? (rollover over the graph for a clue)

When was the growth slowing down?

When was the population constant?