Edexcel International A Level Biology

Revision Notes

6.3 The Bacterial Growth Curve

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The Bacterial Growth Curve

  • Bacteria divide using the process of binary fission during which one cell will divide into two identical cells
  • The process is as follows
    • The single, circular DNA molecule undergoes DNA replication
    • Any plasmids present undergo DNA replication
    • The parent cell divides into two cells, with the cytoplasm roughly halved between the two daughter cells
    • The two daughter cells each contain a single copy of the circular DNA molecule and a variable number of plasmids


Binary fission in bacteria

The process of binary fission produces two identical daughter cells

Bacterial growth curve

  • The growth of a bacterial population follows a specific pattern over time; this is known as a growth curve
  • There are 4 phases in the population growth curve of a microorganism population
    • Lag phase
      • The population size increases slowly as the microorganism population adjusts to its new environment and gradually starts to reproduce
    • Exponential phase
      • With high availability of nutrients and plenty of space, the population moves into exponential growth; this means that the population doubles with each division
      • This phase is also known as the log phase
    • Stationary phase 
      • The population reaches its maximum as it is limited by its environment, e.g. a lack of resources and toxic waste products.
      • During this phase the number of microorganisms dying equals the number being produced by binary fission and the growth curve levels off
    • Death phase
      • Due to lack of nutrients and a build up of toxic waste build up, death rate exceeds rate of reproduction and the population starts to decline
      • This phase is also known as the decline phase 

Standard growth curve of a microorganism

There are four phases in the standard growth curve of a microorganism

Using logarithms in growth curves

  • During the exponential growth phase bacterial colonies can grow at rapid rates with very large numbers of bacteria produced within hours
  • Dealing with experimental data relating to large numbers of bacteria can be difficult when using traditional linear scales
    • There can be a wide range of numbers reaching from single figures into millions
    • This makes it hard to work out a suitable scale for the axes of graphs
  • Logarithmic scales can be very useful when investigating bacteria or other microorganisms
    • The numbers in a logarithmic scale represents logarithms, or powers, of a base number
    • If using a log10 scale, in which the base number is 10, the numbers on the y-axis represent a power of 10, e.g. 1=101 (10), 2=102 (100), 3=103 (1000) etc.
  • Logarithmic scales allow for a wide range of values to be displayed on a single graph
  • For example, if yeast cells were grown in culture over several hours the number of cells would increase very rapidly from the original number of cells present
  • The results from such an experiment are shown in the graph below using a log scale
    • The number of yeast cells present at each time interval was converted to a logarithm before being plotted on the graph
      • This can be done using a log function on a calculator
    • The log scale is easily identifiable as there are not equal intervals between the numbers on the y-axis
    • The wide range of cell numbers fit easily onto the same scale

Yeast log scale graph

When a log10 scale is used, the scale increases by a factor of 10 each time; this allows large increases in numbers to be shown on a single graph

Exam Tip

You won’t be expected to convert values into logarithms or create a log scale graph in the exam. Instead you might be asked to interpret results that use logarithmic scales or explain the benefit of using one! Remember that graphs with a logarithmic scale have uneven intervals between values on one or more axes.

Exponential growth rate constants

  • To calculate the number of bacteria in a population the following formula can be used

N subscript t space end subscript equals space N subscript italic 0 italic space end subscript straight x space 2 to the power of k t end exponent

  • Where
    • Nt = the number of organisms at time t
    • N0 = the number of organisms at time 0
    • k = the exponential growth rate constant
    • t = the time for which the colony has been growing
  • To use this equation the exponential growth rate constant k must be calculated
    • This refers to the number of times the population doubles in a given time period
  • The following formula can be used to calculate the exponential growth rate constant

k space equals space fraction numerator log subscript 10 space N subscript t italic space end subscript italic minus italic space log subscript italic 10 italic space end subscript N subscript italic 0 over denominator log subscript 10 2 space straight x space t end fraction

Worked example

A bacterial colony started with 2 individuals and after 3 hours of growing there were 926 bacteria in the colony.

1. Calculate the exponential growth rate constant of this colony

2. Calculate the number of bacteria in the colony after 5 hours

Step 1: Calculate the exponential growth rate constant

k space equals space fraction numerator log subscript 10 space end subscript N subscript t italic space end subscript italic minus italic space log subscript italic 10 italic space N subscript italic 0 over denominator log subscript 10 2 space straight x space t end fraction

k space equals space fraction numerator log subscript 10 left parenthesis 926 right parenthesis space minus space log subscript 10 left parenthesis 2 right parenthesis over denominator log subscript 10 2 space straight x space 3 end fraction

k space equals space fraction numerator 2.67 over denominator 0.30 space straight x space 3 end fraction

k space equals space 3

Step 2: Calculate the number of bacteria after 5 hours

N subscript t space equals space N subscript italic 0 italic space end subscript straight x space 2 to the power of k t end exponent

N subscript t space end subscript equals space 2 space straight x space 2 to the power of left parenthesis 3 right parenthesis left parenthesis 5 right parenthesis end exponent

N subscript t space end subscript equals 2 space straight x space 2 to the power of 15

N subscript t space end subscript equals space 65 space 536

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Marlene

Author: Marlene

Marlene graduated from Stellenbosch University, South Africa, in 2002 with a degree in Biodiversity and Ecology. After completing a PGCE (Postgraduate certificate in education) in 2003 she taught high school Biology for over 10 years at various schools across South Africa before returning to Stellenbosch University in 2014 to obtain an Honours degree in Biological Sciences. With over 16 years of teaching experience, of which the past 3 years were spent teaching IGCSE and A level Biology, Marlene is passionate about Biology and making it more approachable to her students.