A spoonful of starter puts 4 million lactic acid bacteria into each mL of warm milk…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A spoonful of starter puts million lactic acid bacteria into each mL of warm milk. Each bacterium divides every minutes. Ignore any limit to the growth.
- How many divisions does a bacterium go through in hours?
- How many million bacteria are in each mL after hours?
- After how many hours do the bacteria reach million in each mL?
Need a reminder? The key ideaShow
Lactic acid bacteria (Lactobacillus) ferment lactose to lactic acid and set milk as curd. Baker's yeast, Saccharomyces cerevisiae, ferments sugar to ethanol and carbon dioxide: . Swiss cheese has holes from the carbon dioxide of Propionibacterium. Roquefort cheese is ripened by a fungus. A bacterium that divides every minutes doubles its number times in each hour. For a gas, with L atm per mol per K.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Start: million per mL. One division every min.
Plan. Count the divisions, then double the number that many times.
Step 1. Divisions. divisions.
Step 2. The count. million per mL.
Step 3. The time to reach million. We need . Then divisions. Each takes h, so the time is h.
Answer: divisions; million per mL; h.
Check. After divisions the count is million, and after it is million. So million lies just before the eighth division.
Watch out. A real culture stops growing when food runs out, so the doubling cannot go on for ever.
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