Math in the News: 11/6/11

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In this issue of Math in the News, we look at the listeria bacteria to see why it is so dangerous.

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Math in the News: 11/6/11

  1. 1. 11/6/11
  2. 2. Bacterial GrowthBacterial growth is a function of time. Under the right conditions, an initialpopulation of bacteria will grow exponentially.
  3. 3. Bacterial GrowthBacterial growth is also a function of temperature. Within the range of 40°F and140·F, bacteria will thrive.
  4. 4. Bacterial GrowthAs a result, we can define a piecewise function of two variables that account fordifferent temperatures and can be graphed for different values of t.
  5. 5. Bacterial GrowthHere is an example of both variables at work. Two tomatoes, one refrigerated andone at room temperature, are observed over several days. The tomato at roomtemperature rots, while the other tomato is essentially the same.
  6. 6. Bacterial GrowthThis graph is a model for a scenario in which a food item is refrigerated up to timet0, after which it is brought to room temperature. The food-borne bacteria growexponentially after t0.
  7. 7. Bacterial GrowthWith listeria the situation is different. This type of bacteria will continue to grow evenwhen refrigerated.
  8. 8. Bacterial GrowthThis results in a different piecewise function.
  9. 9. Bacterial GrowthLet’s look at two situations. In each case a canteloupe is refrigerated with theunderstanding that this will keep bacteria from growing. But in one case, thecanteloupe is infected with listeria.
  10. 10. Bacterial GrowthThe flat-line graph represents the canteloupe without listeria, while the other graphshows the dramatic growth for the other canteloupe.
  11. 11. Listeria• The danger of listeria is that it does its work (growing exponentially) under conditions that we think are having the opposite effect.
  12. 12. Bacterial GrowthFor more information on listeria and other harmful bacteria, go to FoodSafety.gov.

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