Question

If cells in exponential growth are dividing every 20 minutes, how long will it take for 2*10^6 cells to become 1.6*10^7?

Answer 1

Solution) We know that the bacterial population grows exponentially, where each single cell divide by binary fission.

formula for population size calculation is N' = No x 2ⁿ

where, N' = population size after time t, No = initial population size and n = total number of generations in time t.

also, n = t/g, where t = total time of growth and g = generation time.

in the given case, we have g = 20min, No = 2x10⁶ , N' = 1.6x10⁷

use the formula above, to find the value of "n".

1.6x10⁷ = 2x10⁶ x 2ⁿ

2ⁿ = 1.6x10⁷ / 2x10⁶

2ⁿ = 8 or 2ⁿ = 2³

n = 3, it means that 3 generations will take.

also, t = n x g = 3 x 20min = 60min.

it means that the initial population of  2x10⁶ will take 60min. to become 1.6x10⁷ , if it is dividing every 20minutes in exponential growth.