Question

Play Keynote Live Table Chart Text Shape Media Comment No x 2n The pathogen Salmonella Typhi has a generation time of 20 minutes in rich media. If you start with 10 bacteria per milliliter, approxim ately how many bacteria would be present in 1 ml after 12 hours (a ssuming unlimited nutrients)? A. 1 x 105 B. 7 x 106 С. 7x108 D. 7 × 1010 E. 7 x 1011

Answer 1

Answer will be E ie 7 x 10¹¹

T₀ = T / n

T₀ = Generation time, T = Time interval in hours or minutes, n = number of generations (number of times population doubles)

T₀ = 20 minutes, T = 12 X 60 = 720 minutes

Applying the formula,

20 = 720/n

n = 720/20 = 36

No. of bacterial cells at a given time is derived by the following formula

N = N₀ x 2ⁿ

N₀ = Number of bacterial cells at the beginning of a time interval

N = Number of bacterial cells at given time

Applying the formula

N = 10 x 2³⁶

2³⁶ = 6.87 x 10¹⁰

N = 10 x 6.87 x 10¹⁰

N = 6.87 x 10¹¹ or 7 x 10¹¹

The answer can also be derived by logrithmic approach. However, to keep the solution simple i have used simple alogrithmic method.