The bacterial growth curve (Core practical 13)

The four phases

1. Lag phase: bacteria adjust to the new conditions, take up water and make enzymes. Little division happens.

2. Log (exponential) phase: nutrients are plentiful; cells divide at a constant rate, doubling each generation.

3. Stationary phase: nutrients run out and toxic waste builds up; the rate of cell division equals the death rate.

4. Death (decline) phase: death rate exceeds division rate as conditions worsen.

Because numbers become huge, the y axis is usually a log scale (log10 of number), on which exponential growth is a straight line.

Exponential growth calculations

After n generations: N = N0 x 2ⁿ

The growth rate constant k is the number of generations per hour:

k = (log10 N - log10 N0) / (0.301 x t)

where t is time in hours and 0.301 = log10 2.

Mean generation time = 1 / k.

Core practical 13

1. Inoculate sterile nutrient broth with bacteria (or yeast) using aseptic technique, and incubate at a constant temperature.

2. At regular intervals, remove a sample aseptically.

3. Measure population size: absorbance using a colorimeter (zeroed with sterile broth), or by serial dilution and plating.

4. Plot the results and calculate k for the exponential phase.

Variables can include temperature, pH or nutrient concentration. Safety: aseptic technique, incubate at 25 °C, disinfect spills, autoclave cultures. Ethics: dispose of microorganisms safely so none are released.

Worked example

A culture grows from 10³ to 10⁶ cells in 5 hours of exponential growth. Calculate k and the mean generation time.

1. k = (6 - 3) / (0.301 x 5) = 3 / 1.505 = 1.99 generations per hour
2. Mean generation time = 1 / 1.99 = 0.50 h

Answer: k = 1.99 per hour; mean generation time about 30 minutes.

Check yourself

1. A culture starts with 500 bacteria. How many are there after 6 generations of exponential growth?
   Show answer

   32000. 500 x 2⁶ = 500 x 64 = 32 000.

2. A population grows from 2 x 10⁴ to 6.4 x 10⁵ cells in 2.5 hours. Calculate k in generations per hour to 2 decimal places.
   Show answer

   2.00. log10 ratio = log10 32 = 1.505; k = 1.505 / (0.301 x 2.5) = 2.00.

3. A culture has a growth rate constant of 2.5 generations per hour. What is the mean generation time in minutes?
   Show answer

   24 minutes. 1 / 2.5 h = 0.4 h = 24 minutes.

4. Why is there little increase in cell number during the lag phase?
   • Cells are adjusting, absorbing water and making enzymes before dividing
   • All the nutrients have been used
   • Toxic waste has built up
   • The death rate exceeds the division rate
   Show answer

   Cells are adjusting, absorbing water and making enzymes before dividing. Cells must prepare before division can start.

5. What causes the stationary phase?
   • Cells are adjusting to new conditions
   • Nutrients are in excess
   • Nutrients run out and waste builds up, so division rate equals death rate
   • The culture is being diluted
   Show answer

   Nutrients run out and waste builds up, so division rate equals death rate. Resources limit growth.

6. Why is a log scale used for the y axis of a growth curve?
   • Numbers increase by huge factors, and exponential growth becomes a straight line
   • It makes the lag phase disappear
   • It shows only dead cells
   • It removes the need to count cells
   Show answer

   Numbers increase by huge factors, and exponential growth becomes a straight line. Log scales handle very large ranges.

7. In core practical 13, what is the colorimeter zeroed with?
   • Distilled water containing bacteria
   • The most concentrated culture
   • Sterile nutrient broth
   • Iodine solution
   Show answer

   Sterile nutrient broth. Zeroing with sterile broth means any absorbance is due to cells.

Practise with instant feedback Print this lesson

Sources

• Pearson Edexcel International Advanced Level in Biology specification (XBI11/YBI11, first teaching 2018)
• Labster Theory: Growth rate constant

Last updated 7 November 2026. Spotted a mistake? Tell us.