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

Looking at data

Look to the right below... wow, that was fast. Now we have some typical data on meningococcal bacteria grown in the lab. Maybe we can use this to figure out how long it takes for meningococci to double their population -- and from there we can tell how long "21 generations" is. But it's hard to interpret just numbers, so let's try putting it on a graph.

Hmm, that is one ugly graph. All the numbers are either way at the bottom or way at the top. I can hardly make out anything.

It would be nice if we could spread the numbers out a little more... and in fact we can. We need to use graph paper with a "log" scale on the y axis, instead of a regular scale. Since logs tell you the magnitude of a number, they do a better job of spreading out a wide range of values. Let's try that now:

(If you don't remember how to make a log-transformed graph, you can review it here)

OK, now we have a graph that looks reasonable. This kind of graph is called "log-transformed."

What happens is a series of numbers that are evenly spaced on a linear scale get spaced differently on a log scale: specifically, on a log scale, the largest numbers get squished together, while the smallest numbers get stretched apart.