Question

Question #e6a1f

Answer 1

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!