Mathematical Modeling of Bacterial Growth

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Updated on Sep 22, 2011

Grade Level: 9th to 12th; Type: Mathematics/Computer Science


Use mathematical modeling to represent and predict future bacterial growth.

Research Questions:

  • Does bacterial growth fit a simple mathematical model?
  • Can future bacterial growth be predicted with computational modeling?

This experiment will introduce students to the mathematical modeling of biological processes. Students will fit the growth pattern of bacteria to a mathematical model and predict future colony expansion.


  • Computer
  • Graphing software (eg, Microsoft Excel)
  • Notebook for recording results
  • Sterile swabs
  • Sterile gloves
  • Prepared nutrient agar in sterile plates

Experimental Procedure

  1. Prepare six sterile plates containing nutrient agar.
  2. Put on sterile gloves (do not touch any non-sterile surface when wearing gloves).
  3. Swab an item with a sterile swab (do not touch anything else with the swab). You can swab anything that contains bacteria like a frequently used surface in your house or your mouth.
  4. Remove the top of the petri dish. Keep the top of the dish in your hand away from any non-sterile surface.
  5. Gently run the swab back and forth in a zigzag pattern on the surface of the agar plate. Do not touch any part of the agar twice.
  6. Put the top of the petri dish back on and label.
  7. Change your gloves.
  8. Repeat steps 3-7 five more times using a new agar plate each time.
  9. Place the petri dishes in an environment that is as close to 37ºC as possible. Bacteria will take longer to grow at room temperature. Ensure that all petri dishes are placed in the same location.
  10. Photograph plates at defined intervals of time (eg, after 24 hours, 36 hours, 48 hours, 60 hours, and 72 hours, 84 hours, 96 hours, etc…).
  11. Count the bacterial colonies on each plate at each time point. Record your results.
  12. Graph the growth data you gather for each agar plate on a scatter plot. The time points will constitute the X-axis and the colony counts will be the Y-axis.
  13. After the data points are plotted, add a trendline to your data. For example, if you are using Microsoft Excel, right-click on a data point on the graph and select “Add Trendline.” In the box that appears, select “Exponential,” “Display equation on chart,” and “Display R-squared value on chart.” Your graph should now show the exponential equation representing the bacterial growth.
  14. Look at the R-squared value. How close is it to one? This number represents how well your data fits the exponential model. The closer it is to 1, the better your data fits in the model.
  15. How much does your equation vary from plate to plate? Are some plates a better fit to the exponential model? What could account for this result?
  16. Input a future time point into the equation you get for each agar plate. The Y-value of the equation will predict the number of bacterial colonies at this time point. 17. Manually count your bacterial colonies at this time point. How accurate is your model’s prediction?

Terms/Concepts: Growing bacteria on agar; counting bacterial colonies on agar plates; mathematical modeling; exponential growth “Exponential Growth and Decay.”

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