A cafeteria worker who fails to wash his hands thoroughly and fails to wear gloves inoculates a quiche with 4 E. coli when he uses his finger to test whether it is done. By the time you purchase the quiche, there are 128 E. coli cells in it. How many generations did the cells go through?

5 generations

Step-by-step explanation:

Data provided in the question:

Number of bacteria at the beginning of a time interval, B = 4

Number of bacteria at the end of the time interval, b = 128

Now,

The relation between the bacteria at the beginning, bacteria at the end and the number of generations (n) is given as:

b = B * 2ⁿ

Therefore,

on substituting the respective values, we get

128 = 4 * 2ⁿ

or

2ⁿ = 32

or

2ⁿ = 2⁵

or

n = 5

hence,

5 generations