Discussion
A penicillin sensitive Escherichia coli population is exposed to a lethal dose (200 µg/ml) of penicillin. Assuming density-independent mortality, which one of the following relationships would describe the number of surviving bacteria (N) over time (T)?
Answer: A
The survivors decline exponentially.
Density-independent mortality means each cell has the same chance of dying per unit time, regardless of how many cells remain. The death rate is then proportional to the number of survivors:
\[ \begin{aligned} \frac{dN}{dT} &= -kN \\ N &= N_{0}\,e^{-kT} \end{aligned} \]
The same fraction is killed in each interval, which is why antibiotic killing curves are straight lines on a log scale. A linear fall would need a constant number killed per unit time; a sigmoidal curve describes density-dependent growth with a limit; and a parabola does not arise from a constant per-cell death rate.
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