Table of Contents

• Section 1. Frank's Story
• 1: The story
• 2: Biological interlude
• Section 2. How the meningitis population grows
• 3: How many meningococci can kill you?
• 4: Build the basic growth equation
• 5: Draw exponential growth
• Section 3. So why isn't Frank dead already?
• 6: How long has poor Frank got?
• 7: All we need now is data
• 8: Looking at data
• 9: Log transform straightens out exponential growth
• 10: Do ALL curves get "straightened" by taking the log?
• 11: Phases of bacterial growth
• Section 4. How can we tell when the population is growing exponentially?
• 12: A test for exponential growth
• 13: And the answer is...
• 14: No way its growing that fast!
• 15: Some more practice
• 16: In search of ... the exact doubling time
• 17: Finding doubling time with messy numbers
• 18: Logs = Exponent-busters
• 19: Let's bust some exponents
• 20: Let's bust some exponents
• 21: Extended problem #1: Exponential growth ends (with a whimper)
• Section 5. Back to Frank
• 22: Extended Problem #2: How long DOES poor Frank have?

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?