# Extended Problem: How long DOES poor Frank have?

So, back to the grindstone. Let's figure out what to do about poor Frank.

Based on lab tests, Frank has 80 meningococci per mL of blood at 9am. Assuming he got infected by a single cell at 5pm, then

1. What is the doubling rate of the meningococci cells?
2. How long does Frank have before he reaches the LD50?

### doubling rate?

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• I need a hint ... :
80 / mL * 5000 mLs = 400,000 cells
• ...another hint ... :
400,000 = 1 * 2^g, so g = log(400,000)/log(2) = 18.6
• I need a hint ... :
5pm to 9am = 16 hours = 960 min
• I need a hint ... :
960 minutes / 18.6 doublings = 51.6 minutes/doubling

### How long does he have until he reaches the 2.5 million cell level (equivalent to the LD50)? In other words, how many more doublings will it take?

(To make this problem interactive, turn on javascript!)

• I need a hint ... :
2,500,000 = 400,000 * 2^g, or 6.25 = 2^g
• ...another hint ... :
2.6 more doublings to go
• ...another hint ... :
2.6*51.6 = 134 minutes

#### I think I have the answer: a little over 2 hours

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