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

How many meningococci can kill you?

So we've established that meningitis is caused by Neisseria meningitidis, which are currently running around like crazy in Frank's bloodstream. Because this disease has been researched extensively, doctors can even tell you how many bacterial cells you need to have in your blood before you're likely to die.

LD50 = 500 cells/mL blood

"LD" means "lethal dose", and 50 means that 50% of the time, someone exposed to this dose will die. So basically, if your blood has 500 of the bacterial intruders per mL, you have about even chances of dying from meningitis. Above 500 per mL and you're even more likely to die.

We can scale up from here to figure out how many bacterial cells Frank's body can handle before it's likely to kill him.

So now we know that by the time that Frank has about 2.5 million meningococci in his body, he's likely to be toast.

Frank vaguely remembers from first year biology that bacteria can grow exponentially, but in his current less-than-stellar state, he doesn't quite remember how that works. Let's refresh his memory...