Culture calculationsSpec 4.1.1.6
Number of bacteria after a certain time
You should be able to calculate the number of bacteria in a population after a certain time if you are given the mean division time. Each division doubles the population.
- Work out the number of divisions: total time ÷ mean division time (use the same units).
- Number of bacteria = starting number × 2 to the power of the number of divisions.
Bacterial population
A single bacterium divides every 20 minutes. How many bacteria are there after 2 hours?
- 2 hours = 120 minutes. Number of divisions = 120 ÷ 20 = 6.
- Number of bacteria = 1 × 2⁶ = 64.
Answer: 64 bacteria
Higher tier
Standard form
A single bacterium divides every 20 minutes. How many bacteria are there after 8 hours? Give your answer in standard form to 2 significant figures.
- 8 hours = 480 minutes. Number of divisions = 480 ÷ 20 = 24.
- Number of bacteria = 2²⁴ = 16 777 216.
- Move the decimal point 7 places: 1.6777216 × 10⁷. To 2 significant figures: 1.7 × 10⁷.
Answer: 1.7 × 10⁷ bacteria
Areas of colonies and clear areas
You should be able to calculate the cross-sectional area of colonies, or of clear areas around colonies, using πr². The radius is half of the diameter.
area = π × r²
Area of a clear zone
The clear zone around an antibiotic disc has a diameter of 14 mm. Calculate its cross-sectional area. Use π = 3.14.
- Radius = 14 ÷ 2 = 7 mm.
- Area = π × r² = 3.14 × 7 × 7 = 3.14 × 49 = 153.86 mm².
Answer: About 154 mm²