Question

5. How many cells will there be if a bacterial culture starts with 50,000 cells and grows exponentially for 8 hours if the culture has a generation time of 30 minutes? Please explain and show work

Answer 1

The bacterial growth in the exponential growth phase will be by geometric progression i.e.. 1, 2, 4, 8, 16 etc. It can be represented as  20, 21, 22, 23,24....................2n, where 'n' will be the number of generations. The equation to calculate the total number of bacterial cells is given below.

Total number of cells after 'n' generations = 2n x initial number of bacteria in the culture.

In the given question, generation time is 30 minutes.

Thus, the number of times the bacteria divides in 8 hours (480 minutes) = 480 / 30 = 16.

Number of generation 'n' = 16.

Initial number of bacterial cells = 50000

If we substitute the values the equation will become as follows:

Total number of cells after 16 generations = 216 x 50000

= 65536 x 50000

= 3276800000 = 3.2768 x 109

Hence, there will be 3.2768 x 109 bacterial cells in the culture after 8 hours of exponential growth.