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

A test for exponential growth

Actually, it's 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?