Bacterium called pathogen. The example of a beaker with a single bacterium in it. That divides and doubles itself. If you place the first bacterium into the beaker, how much time it takes to half full? And how much time it takes to full?
if we put a bacteria in 720 milliliter jar.
To calculate the time it takes for the beaker to become half full and completely full, we need to know the growth rate or doubling time of the bacterium.
Let's assume that the doubling time of the bacterium is 20 minutes. This means that the bacteria double in number every 20 minutes.
To calculate the time it takes for the beaker to become half full, we need to determine the number of times the bacterium needs to divide to reach half the volume of the jar.
1. Initially, we have 1 bacterium in a 720 milliliter jar.
2. After 20 minutes, the bacterium will divide, resulting in 2 bacteria. The total volume remains the same.
3. After 40 minutes, each of the 2 bacteria will divide again, resulting in 4 bacteria. Again, the total volume remains the same.
4. This doubling process continues, and after a certain number of divisions, the total number of bacteria will reach half of the jar volume.
To calculate the number of divisions required, we can use the formula:
(Number of bacteria) = 2^(n)
Where 'n' represents the number of divisions.
To find 'n', we need to solve the equation:
2^(n) = (jar volume / initial bacteria count)
Substituting the values:
2^(n) = (720 / 1)
Taking the logarithm of both sides of the equation:
n = log2(720)
Using a calculator, we can find that n is approximately 9.5.
Since 'n' represents the number of divisions, and each division takes 20 minutes, we can calculate the time it takes to reach half the volume:
Time to reach half full = 9.5 divisions * 20 minutes per division = 190 minutes.
To calculate the time it takes to fill the entire jar, we need to continue the doubling process until the number of bacteria equals the capacity of the jar.
Again using the formula:
2^(n) = (jar volume / initial bacteria count)
Substituting the values:
2^(n) = 720
Taking the logarithm of both sides:
n = log2(720)
Calculating n gives us approximately 9.5.
So, the time it takes to fill the entire jar is:
Time to fill the jar = 9.5 divisions * 20 minutes per division = 190 minutes.
Therefore, it would take approximately 190 minutes (3 hours and 10 minutes) to reach half full and another 190 minutes (3 hours and 10 minutes) to fill the entire jar.
To determine how long it takes for a beaker with a single bacterium to reach half full, and then full, we need to consider the rate at which the bacterium multiplies.
Let's assume that the bacterium doubles in number every hour. In this case, we can calculate the time it takes to reach half full by working backwards.
Since the bacterium doubles every hour, it means that it divides once after the first hour, resulting in two bacteria. After the second hour, each of the two bacteria divide again, giving a total of four bacteria. Continuing this pattern, after n hours, the number of bacteria is represented by 2^n.
Now, we know that the beaker is initially filled with just one bacterium, and we want to know how long it takes to reach half full, which means having 360 milliliters of bacteria.
Let's solve the equation 2^n = 360 to find the value of n. Using logarithms, we have:
n = log2(360) ≈ 8.5
So, it would take approximately 8.5 hours for the beaker to be half full, assuming the bacterium doubles every hour.
To calculate the time it takes for the beaker to be completely full, we need to repeat the same process, but start with the initial volume of the beaker, which is 720 milliliters.
Using the same equation, 2^n = 720, we can solve for n:
n = log2(720) ≈ 9.5
Thus, it would take approximately 9.5 hours for the beaker to be completely full.
It's important to note that these calculations assume ideal conditions and growth patterns, and in reality, multiple factors may affect bacterial growth rates.