Question

In a sample, the growth of microbial cells started with an initial concentration of \(5 \times 10^4\) cells per millilitre (mL) of the sample. After a certain time period, the cell concentration was found to be \(1280 \times 10^4\) cells per mL of the sample. Assuming binary fission of cells and no cell death, the number of generations of cell growth occurred in this time period is _______ (answer in integer).

Hint:

For binary fission, the number of generations is calculated using the logarithmic growth formula based on initial and final cell concentrations.

Answer 1

Correct Answer: 8

The number of generations is given by the formula: \[ N = \frac{\log \left( \frac{N_f}{N_0} \right)}{\log 2} \] where:
- \( N_f \) is the final concentration of cells,
- \( N_0 \) is the initial concentration of cells.
Substituting the given values: \[ N = \frac{\log \left( \frac{1280 \times 10^4}{5 \times 10^4} \right)}{\log 2} = \frac{\log (256)}{\log 2} = 8. \] Thus, the number of generations is \( 8 \).