Some more practice
There are fast and exact ways to solve these kinds of problems (if you remember your algebra), and there are slower and less exact ways (if you don't). Either way is fine here, although the hints will only be for the non-algebra option.
What if exactly 3 Vibrio were initially present in the sample? In that case, how long would it be before the critical level of 1 million organisms was reached?
(To make this problem interactive, turn on javascript!)
- I need a hint ... :
Remember the equation: N0x 2^n - ...another hint ... :
In this case, the initial population size (N0) is 3. - ...another hint ... :
If you don't remember algebra, you just have to start guessing. - ...another hint ... :
We know it should be less than 20 generations. - ...another hint ... :
Let's try 15 generations: 3×2^15 = approx 98,000. Not enough. - ...another hint ... :
3×2^18 = 786,432, but 3×2^19 = about 1.6 million.
I think I have the answer: between 18 and 19 generations
The guess-and-try method is fine, if a little slow. However, if you understand how doubling works, you can make some intelligent guesses and speed up your answers. For example, if 1 million cells require 20 generations, what would 500,000 cells require?
With that in mind, try the next problem.
What if the infective dose was 105? In that case, how many generations would it take to get to that number?
(To make this problem interactive, turn on javascript!)
- I need a hint ... :
We only need 1/10 the cells (that is 100,000 cells instead of 1 million) - ...another hint ... :
1/10th is about 3-4 less doublings...
I think I have the answer: 16 to 17 generations
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