Question #e6a1f

1 Answer
Ernest Z.
Sep 27, 2014

It would take about 42 h.

This involves several assumptions. Here are mine:

  • The mass of a bacterium is 1 × 10⁻¹⁵ kg.
  • The mass of a human is 70 kg.
  • There is only exponential growth, with no lag phase or stationary phase.

The equation for exponential growth is

#N_t = N_0 × 2^(t/t_"d")# where

#N_t# is the number (mass) at time #t#
#N_0# is the number (mass) at time #t# = 0
#t_"d"# is the division time (analogous to half-life in exponential decay)

This gives

#ln(N_t/N_0) = (t/t_"d") ln2# and

#t = (t_"d"/ln2) ln(N_t/N_0)#

#t = ("45 min"/ln2) ln("70 kg"/(1× 10^-15 "kg")) = 64.9 min × ln(7 × 10^16)# =
64.9 min × 38.8 h = 2520 min = 42 h (2 significant figures)

Scary!

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