Bacteria reproduce by binary fission: one cell splits into two. With enough nutrients and a suitable temperature this can happen every 20 minutes or so: the mean division time.

number of bacteria = starting number × 2ⁿ (n = number of divisions)
n = time ÷ mean division time

1. 50 bacteria, divide every 30 minutes, for 3 hours
2. 3 hours = 180 minutes; 180 ÷ 30 = 6 divisions
3. 50 × 2⁶ = 50 × 64 = 3200 bacteria

Big answers go in standard form (Higher): 100 × 2²⁰ = 104 857 600 = 1.05 × 10⁸.

Bacteria are grown in a nutrient broth or on agar in a Petri dish. Every step keeps unwanted microorganisms out:

• sterilise dishes and agar before use; pass the inoculating loop through a flame
• lift the lid only a little when adding bacteria
• tape the lid on, but not all the way round, so oxygen gets in and harmful anaerobic bacteria do not grow
• store the dish upside down so condensation does not drip on the agar
• in school, incubate at 25 °C at most, so pathogens that like body temperature are unlikely to grow

Spread bacteria over agar, add paper discs soaked in different antibiotics or antiseptics (and one in sterile water as a control), incubate, then measure the clear zone around each disc. A bigger clear zone means more bacteria killed.

area of clear zone = π r² (r = diameter ÷ 2)

1. Clear zone 14 mm across: r = 7 mm
2. π × 7² = π × 49 = 153.9... = 154 mm² (3 s.f.)

Halve the diameter first. Squaring the diameter makes the area four times too big.