MathBench > Microbiology

Frank's Football Fiasco

How long has poor Frank got?

Frank's noseAn amazing thing about meningitis is that the initial infection can be caused by a SINGLE CELL. Despite the thousands that are probably holed up in Frank's nose and throat, despite the spectacular nosebleed, despite everything, Frank's immune system has done and great job and let just one tiny cell survive.

So, how many doublings (or generations) does the cell have to go through to get to 2.5 million? (Remember, 2.5 million is the LD50 scaled up for 5 liters of blood).

Here's a likely but vague answer: probably not as many as you think. Let's try some numbers. You can play along at home using a calculator, or just click the buttons to see the answer:

10 generations:

20 generations:

30 generations:

The magic number is 2.5 million, and by 20 generations, Frank's already got over 1 million. Double that and you're already past the 2 million mark. So, basically, Frank's got a little over 21 generations... however long that is...