Starting with a single cell, how long (in hours) will it take for the mass of an E. coli culture to equal that of the Earth? Assume exponential phase and limitless nutrients.

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.