AQA GCSE Calculating Bacterial Populations (Biology)

Calculating Bacterial Populations

Bacteria divide by a process called binary fission.

Under ideal conditions of a suitable temperature and plenty of nutrients they can divide as often as once every 20 minutes.

Mean Division time

Mean Division Time (MDT) is the average time it takes for a bacterial cell to divide into two new cells.

It’s the same as the generation time.

The shorter the mean division time, the faster the bacterial population will grow.

Example: If the MDT of E. coli is 20 minutes, then every 20 minutes each cell divides, so the population doubles.

Formula to calculate population size

Example question.

1.A culture of bacteria has a mean division time of 40 minutes. Starting with 1 bacterium, how many bacteria will there be after 4 hours?

n = total time/mean division time

Total time = 4 hours or 240 minutes

n = 240/40 = 6 divisions

N= N₀ x 2ⁿ

N = 1 x 2⁶ = 64

N= 64

Using Standard Form

Standard form is used to make the writing of very small or very large numbers easier.

Writing large numbers in Standard form.

The number 1 million can be written in standard form, by moving the decimal point which is just after the 6th zero, 6 places to the left.

Writing small numbers in standard form.

The number 0.000001 can be written in standard form by moving the decimal point 6 places to the right.

Example question

A bacterium has a mean division time of 20 minutes. Starting with 5 bacteria, how many will there be after 24 hours? Give your answer in standard form.

24 hours = 24 × 60 = 1440 minutes

n = 1440/20 = 72 divisions

N= N₀ x 2ⁿ

N = 5 x 2⁷² = 2.4 x 10²²

Practice Question

1.State the name of the process that bacteria use to divide.

2. Under ideal conditions what would be the mean division time?

3. State the formula used to:

3a. Calculate new population size

3b. Calculate number of divisions

4.A bacterial culture starts with 2 bacteria. The mean division time is 30 minutes. How many bacteria will there be after 3 hours?

5.A bacterial culture starts with 1 bacterium. The mean division time is 15 minutes. How many bacteria will there be after 6 hours? Express your answer in standard form.

6.A bacterial culture has a mean division time of 20 minutes. If the population grows to 512 cells after 2 hours, how many bacteria were there at the start?