Table of Contents

• Section 1. How the meningitis population grows
• 1: How many meningococci can kill you?
• 2: Build the basic growth equation
• 3: Draw exponential growth
• Section 2. So why isn't Frank dead already?
• 4: How long has poor Frank got?
• 5: All we need now is data
• 6: Looking at data
• 7: Log transform straightens out exponential growth
• 8: Do ALL curves get "straightened" by taking the log?
• 9: Phases of bacterial growth
• Section 3. How can we tell when the population is growing exponentially?
• 10: A test for exponential growth
• 11: And the answer is...
• 12: No way its growing that fast!
• 13: Some more practice
• 14: Extended problem: Exponential growth ends
• 15: Review

Log transform straightens out exponential growth

 

What we did on the graph is called log transformation, which is a very powerful tool in biology, even if it cannot transform 18-wheelers or pickups trucks into sentient beings.

What you do when you log-transform data is change the scale of the data. Normal everyday data is usually expressed on a graph with a linear scale. Linear means that each tickmark on the axis increases the number by the same amount -- for example, the tickmarks might stand for 0, 5, 10, 15, etc.

However, our bacterial population is not increasing by the same amount in each timestep. Starting with 1 cell, in the first timestep we add 1 more, in the second timestep we add 2 more, in the third timestep we add 4 more, and so on. The graph does not look like a straight line.

 

When you transform data, you are putting it on a log scale, which is also called a multiplicative scale. The tickmarks on a multiplicative scale represent numbers that differ by the same FACTOR, or multiplier. And in fact our bacterial populations also differ by the same factor at each timestep -- they double, or increase by a factor of 2.

So when you use a log scale, populations separated by the same factor will line up in a straight line. The slope of that line will depend on how big the multiplying factor is, which we'll talk about in a few screens. But the crucial point is:

When logtransformed:

ANY population that grows or shrinks by a constant factor will appear as a straight line (pointing up or down)

ANY population that is constant will appear as a flat line.