If a bacteria reproduced every 5 minutes and you start with one at noon, how many will you have after one hour?
I will assume by "reproduced every 5 minutes"
you mean "double every 5 minutes)
so in one hour we would have a "doubling" taking place 12 times
noon -- 1
5 minutes later -- 2 , or 2^1 --- first doubling
10 minutes later --4 or 2^2 --- 2nd doubling
..
60 minutes later ---2^12 ------15th doubling
2^12 = 4096
over 4,000 germs.
To get the answer to this question, we need to figure out how many times the bacteria would reproduce in one hour.
Since the bacteria reproduces every 5 minutes, there are 60 minutes in an hour, so there would be 60 / 5 = 12 intervals of 5 minutes in an hour.
Now, let's calculate how the number of bacteria would increase at each interval:
- At the start, there is 1 bacteria.
- After the first 5 minutes, the bacteria reproduces and there are 2 bacteria (the original one, plus a copy).
- After 10 minutes, each of the 2 bacteria reproduces, resulting in 4 bacteria.
- After 15 minutes, each of the 4 bacteria reproduces, resulting in 8 bacteria.
- And so on, until the end of the hour.
We can see that the number of bacteria is doubling at each 5-minute interval. Since there are 12 intervals in an hour, the bacteria population would double 12 times.
To calculate the final number of bacteria after one hour, we can use the formula: Final number of bacteria = Initial number of bacteria * 2^(number of doublings).
In this case, the initial number of bacteria is 1, and the number of doublings is 12. Substituting these values into the formula:
Final number of bacteria = 1 * 2^12 = 1 * 4096 = 4096.
So, after one hour, starting with one bacteria that reproduces every 5 minutes, you would have 4096 bacteria.