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What are the units of $N$: the colonies of bacteria or the viable cell count?

This is in regards to the bacterial growth formula used during serial dilutions,

$$ N =N(0) e^{kt} \quad . $$

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Either; they're identical to the units of $N(0)$. In $N =N(0) e^{kt}$,

  • $t$ has units of time (days, minutes, whatever you have chosen)
  • $k$ has units of (1/time) (inverse of $t$'s units)
  • $kt$ is thus unitless, as is $e^{kt}$
  • $N$ and $N(0)$ have the same units.
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