THE GROWTH OF YEAST

The laboratory in this conversation, Data from Carlson, asks you to find the logistic model which best matches Carlson's data on the growth of a colony of yeast. The applet here is a modification of Slinky which displays the data together with the solution curve. You can choose values for the two constants k and c and judge by eye how well the curve fits the data. Following the applet, we raise a couple of questions you might like to think about.

Here are two questions to consider:

1. When the authors bake bread, they knead the dough and let it rise. When it has risen sufficiently, they punch the dough down and let it rise again. They find that the second rising is faster, that it takes between one-half and two-thirds the time of the first rising. Does this model of yeast growth support this? (Hint: Not yet it doesn't. What makes the bread rise is carbon dioxide which the yeast produces. The model of yeast growth will need a second variable to represent carbon dioxide. The production rate of carbon dioxide should be proportional to the population of yeast.)

2. The other major culinary use of yeast is in the production of liquor. The carbon dioxide gives beer and champagne their fizz. The alcohol is a waste product of the yeast. We say ``waste'' because it is ultimately lethal to the yeast. That is why wine is never more than 12 or 13% alcohol--alcohol, in concentrations this strong kills yeast. Our challenge to you is to alter your model to include alcohol. (Hint: You will need a new variable for alcohol. Like carbon dioxide, its production rate should be proportional to the yeast population. The interesting part will be in deciding how the alcohol affects yeast growth. How do you fit the new variable into your equation for y'? There are several possible answers.)

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