Answer:
43.6 hours, which is less than two days.
Explanation:
To calculate Growth for an exponentially growing populations
Nt = N▪ * 2^n
Where,
N▪= cell number at initial time
Nt = cell number at later time
n = number of generations
Assuming exponential phase and limitless nutrients
How long until E.coli conquers the earth?
Given,
1 doubling = 20 min = 0.33hr
N▪= Mass = 9.5 x 10^-13 g/bacterium
Nt= Mass = 5.9 x 10^27 g/Earth
Nt = N▪ * 2^n
5.9 x 10^27 = 9.5 x 10^-13 * 2^N
nlog(5.9 x 10^27) = log(9.5 x 10^-13) + nlog(2)
27.7 = -12.0 + n(0.3)
27.7 + 12.0 = n(0.3)
39.7 = n(0.3)
132 = n
Therefore,
132 generations * 0.33 hour/generation = 43.6 hours
43.6 hours is less than two days.
Our answer for a single cell, it will take less than two days for the mass of an E. coli culture to equal that of the Earth on assuming exponential phase and limitless nutrients.
