# Maths - Bacterial calculations

Bacteria reproduce at regular intervals, for example every 20 minutes. This allows mathematical calculations to be undertaken in order to predict how many bacteria will be present in a given time.

## How to calculate the number of bacteria in a population

Question

The mean division time for bacteria population A is 20 minutes. The starting bacteria population of A is 1. 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

Question

Calculate how many times the bacteria divide in 6 hours.

Bacteria divide every 20 minutes, and will divide three times every hour (60 ÷ 20 = 3).

3 × 6 = 18

### Part 2

Question

Calculate the number of bacteria in the population.

Every time the bacteria reproduce, the number doubles. You can use an equation to calculate this.

Bacteria at the end of the growth period = bacteria at the beginning × 2number of divisions of the growth period

Number of bacteria at the beginning = 1

Number of divisions = 18

Using the above equation: 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.

## Additional practice questions

Question

The mean division time for a bacterial population is 30 minutes. Calculate how many bacteria will be present after 8 hours, when starting with 1 bacterium.

2 divisions per hour. 2 × 8 = 16 total divisions, therefore 1 × 216 = 1 × 65,536 which is 65,536 bacteria or 6.55 × 104 bacteria (standard form).

Question

The mean division time for bacteria population C is 20 minutes. Calculate how many bacteria will be present after 2 hours, when starting with 10 bacteria.

3 divisions per hour. 3 × 2 = 6 total divisions, therefore 10 × 26 = 10 × 64 which is 640 bacteria or 6.4 × 102 bacteria (standard form).