Extended Problem: How long before the oysters are unsafe?
So, back to the grindstone. Let's figure out what to do all those oysters.
Based on lab tests, each oyster has 400,000 Vibrio at 9am. Assuming it was infected by a single cell at 5pm, then
- What is the doubling rate of the Vibrio?
- How long till the infective dose of 1 million is reached?
doubling rate?
(To make this problem interactive, turn on javascript!)
- ...another hint ... :
400,000 = 1 * 2^n, so n = 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
I think I have the answer: 52 minutes
If the Vibrio keep multiplying at this rate, how long before they reach the infective dose (1 million)?
(To make this problem interactive, turn on javascript!)
- I need a hint ... :
1 million = 400,000 * 2^n, or 2.5 = 2^n - ...another hint ... :
log(2.5) = n log(2) - ...another hint ... :
rearrange! n = 1.32 doublings required
I think I have the answer: 1.32 doublings * 52 minutes / doubling = 69 minutes
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