A type of bacteria doubles in number every 12 hours. After 2 days, there are 48 bacteria. How many bacteria were there at the beginning of the first day.
I know the answer is 3, but want to know how it arrived at the number "3"
work backwards
since they "doubled" every 12 hours ...
(1/2 day = 12 hours)
at end of 2 days -- 48
at end of 1.5 days -- 24
at end of 1 day -- 12
at end of 1/2 day -- 6
at start ----------- 3
No the right answer
To find the number of bacteria at the beginning of the first day, we can work backwards from the given information.
Let's consider the doubling time of the bacteria, which is 12 hours. Since there are 48 bacteria after 2 days (48 hours), we can divide the total time (48 hours) by the doubling time (12 hours) to find out how many times the bacteria doubled.
48 hours / 12 hours = 4
This means that the number of bacteria doubled four times over the 2-day period. Now let's work backwards to determine the initial number of bacteria. If the bacteria doubled four times, it means we need to divide the final number of bacteria (48) by 2 four times:
48 / 2 = 24
24 / 2 = 12
12 / 2 = 6
6 / 2 = 3
Therefore, there were 3 bacteria at the beginning of the first day.
To find out how many bacteria were there at the beginning of the first day, we can work backwards from the given information.
We know that the number of bacteria doubles every 12 hours, and after 2 days (which is 48 hours), there are 48 bacteria. So, we can divide the total number of bacteria by the number of times it doubles to find the starting amount.
Since the bacteria doubles every 12 hours, we need to determine how many times it doubles in 48 hours. We can divide 48 by 12 to get 4. This means the bacteria doubles 4 times in 48 hours.
Now, if we have 48 bacteria after 4 doublings, we can determine how many bacteria we had before the first doubling. To do this, we divide the final amount (48) by 2 raised to the power of the number of doublings.
In this case, we divide 48 by 2^4 (which is 2 raised to the power of 4). Calculating 2^4, we get 16. So, 48 divided by 16 is equal to 3.
Hence, there were 3 bacteria at the beginning of the first day.