Bacterial calculations

• Vaccinations allow protection against specific diseases, but the level of protection depends on the amount of people vaccinated.
• Some diseases can be treated with antibiotics.
• Bacteria reproduce at regular intervals, an example might be every 20 minutes.
• This allows mathematical calculations to be undertaken in order to predict how many bacteria will be present in a given time.
• The mean division time for bacteria population A is 20 minutes.
• If the observation begins with one bacteria, calculate how many bacteria will be present after 6 hours.
• In order to answer this, you can split the calculations into two sections.
• Part 1: Calculate how many times the bacteria divide in 6 hours.
• If the bacteria grow for 6 hours, each bacterium will divide 3 times per hour × 6 hours = 18 times.
• For a higher mark, answers can be expressed in standard form.
• To calculate the number of bacteria after 2 hours, starting with 10 bacteria, divide 60 minutes by 1 division every 20 minutes, which is 3 divisions per hour.
• Every time the bacteria reproduce, the number doubles.
• The total number of divisions after 2 hours is 6, therefore 10 × 2 6 = 10 × 64 which is 640 bacteria or 6.4 × 10 2 bacteria in standard form.
• The mean division time for a bacterial population is 30 minutes.
• To calculate the number of bacteria after 8 hours, starting with 1 bacterium, divide 60 minutes by 1 division every 30 minutes, which is 2 divisions per hour.
• The total number of divisions after 8 hours is 16, therefore 1 × 2 16 = 1 × 65,536 which is 65,536 bacteria or 6.55 × 10 4 bacteria in standard form.
• The mean division time for bacteria population C is 20 minutes.
• An equation can be used to calculate the number of bacteria in a population.
• The number of bacteria at the end of the growth period is equal to the number at the beginning multiplied by 2, and the number of divisions of the growth period is also equal to the number at the beginning.
• The answer of 262,144 bacteria can also be written as 2.62 × 10 5 bacteria.