Prep Activity 10.1.1.
The bacteria lactobacillus acidophilus is part of turning milk into yogurt. Based on experiments, a new generation of bacteria are formed every 70 minutes, that is, the population doubles every 70 minutes. Suppose when we start tracking the data we have 3 g of cells, and that the mass of the cells doubles when the population doubles. (It’s more realistic to measure the mass of our bacteria colony than to try to count thousands of bacteria cells!)
(a)
Fill in the table below.
| Minutes, \(t\) | 70-minute Periods, \(n\) | Colony Mass (g), \(M\) |
|---|---|---|
| 0 | 0 | 3 |
| 70 | 1 | |
| 140 | 2 | |
| 210 | ||
| 280 | ||
| 350 |
(b)
What is the change factor for the colony’s mass? What is the percent change?
(c)
(d)
Use your formula to find the mass of the colony after 700 minutes, i.e., after 10 70-minute periods.
(e)
Use your formula to determine how long it takes for the mass of the colony to reach 1 kg, i.e., 1000 g.
(f)
Suppose we want to know the mass of the colony after 6 hours. How easy is it to use your formula to figure this out? Explain your answer.
