Table of Contents

• Prequiz...
• 1: Logs of graphs and Graphs of logs
• 2: Method 1: Log, then graph
• 3: The curvy line turned into a straight line!
• 4: To transform or not to transform?
• 5: Method 2: graph, then log
• 6: Graphing bigger (and smaller) numbers
• 7: Try it out
• 8: Just add realism
• 9: Review

The curvy line turned into a straight line!

You probably noticed the curvy line on the original graph turned into a straight line on the log transformed graph.

 

Why does this happen? Consider the following 2 facts:

1. In real life, every time 12 hours passes, the bacteria increase by a factor of 10.

2. In math life, every time you move up a log unit, you're increasing the magnitude of the original measurement by a factor of 10.

So, taking the log accounts for the multiplying nature of bacterial growth, and all you're left with on the graph is a straight line, pointing upwards.

When growth happens by multiplying the population by a constant number each timestep, we call that exponential growth. And any time you have exponential growth, taking the log of the population size will turn the graph into a straight line. This is true even if the constant multiplier is not 10 -- in that case, your straight line will have a different slope, but it will still be straight.