Question

E. Coli has a doubling time of 20 minutes under certain growth conditions. Compute the biomass of E. coli (in pounds) that will accumulate when a single cell of E. coli grows exponentially for 50 hours in these conditions, assuming that nutrients are not limiting.   Show your work.

(An E. Coli cell has a mass of 10^-12gram/cell).

Answer 1

Nt= N02^t

t= number of generations

time taken= 50 hours= 50 $\times$ 60= 3000 minutes

generation time= 20 minutes

number of generations= 3000/20=150 generations

N0= 1

Nt= 1 $\times$ 2^150

= 1.43$\times$10^45 cells

mass of a cell= 10^-12 g

mass of 1.43$\times$10^45 cells = 1.43$\times$10^45 $\times$ 10^-12 = 1.43 $\times$ 10^33 g

1 kg = 1000 g

1.43 $\times$ 10^33 g = 1.43 $\times$ 10^33 g/1000=1.43$\times$10^30 kg

1 Kg=2.20462 pounds

1.43$\times$10^30 kg = 1.43$\times$10^30 kg/ 2.20462 = 6.5 $\times$ 10^29 pounds

mass of the cells after 50 hours in punds= 6.5 $\times$ 10^29 pounds