Calculating growth
Bacteria reproduce at regular intervals. An example might be every 20 minutes. This allows mathematical calculations to be made in order to predict how many bacteria will be present in a given time.
How to calculate the number of bacteria in a population
Example
The mean division time for bacteria population A is 20 minutes. If the observation begins with one bacterium, calculate how many bacteria will be present after six hours.
In order to answer this, you can split the calculations into two sections.
Part 1 – Calculate how many times the bacteria divide in six hours
In this example, the bacteria divide every 20 minutes, and will therefore divide three times every hour, \(\frac{60}{20}\) = 3.
If the bacteria grow for six hours, each bacterium will divide 3 times per hour × 6 hours = 18 times.
Part 2 – Calculate the number of bacteria in the population
Every time the bacteria reproduce, the number doubles. To calculate the number of bacteria at the end of the growth period, you can use this equation.
Number of bacteria at the beginning = 1
Number of divisions = 18
1 × 218 = 1 × 262,144 = 262,144 bacteria
For a higher mark, you could express answers in standard form.
For example, the above answer of 262,144 bacteria can also be written as 2.62 × 105 bacteria.
Question
The mean division time for a bacterial population is 30 minutes. Calculate how many bacteria will be present after eight hours, when starting with one bacterium.
If after every 30 minutes there is one division, then after 60 minutes (one hour) there are two divisions.
8 hours × 2 divisions = 16 divisions in total.
Therefore, 1 × 216 = 1 × 65,536, which is 65,536 bacteria, or 6.55 x 104 bacteria in standard form.
Question
The mean division time for a bacterial population is 20 minutes. Calculate how many bacteria will be present after two hours, when starting with 10 bacteria.
1 division every 20 minutes = 3 divisions per 60 minutes.
2 hours × 3 divisions = 6 divisions in total.
Therefore, 10 × 26 = 10 × 64 which is 640 bacteria, or 6.4 x102 bacteria in standard form.
Slowing bacterial growth
As shown above, the exponential growth of bacteria can give very large numbers of bacterial cells in short periods of time. It is important, where food storage is concerned, that we are able to slow this process to prevent spoilage.
The rate at which bacteria divide can be reduced by reducing the temperature. Keeping food in the refrigerator slows bacterial growth and food can be kept for longer before spoiling.
If food is frozen, then bacterial growth stops. However, the bacteria are not killed, so any increase in temperature would increase bacterial growth.
Cooking food at a very high temperature will kill bacteria.