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2 December, 15:10

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.

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  1. 2 December, 15:33
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    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.
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