Question 7 of 12: Bacterial Growth Curve

Question 7: Bacterial Growth Curve (16.7 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Bacterial count spans four orders of magnitude here, so the appropriate plot is semi-log (count on a log axis, time on a linear axis) — a straight-line segment on this axis directly identifies the exponential (log) phase.

(i) Growth curve and phase boundaries

Approach. Compute the interval-to-interval doubling time $t_d = \Delta t\,\ln 2/\ln(N_2/N_1)$ across the data; phases are identified from where $t_d$ is short and constant (exponential growth), long or undefined (lag/stationary), or where the count falls (death).

1. Lag phase, 0–1 h. Count is flat at $1(10^6)$/mL — no increase, $t_d$ undefined.
2. Exponential (log) phase, 1–12 h. Doubling time is short and essentially constant across every sub-interval: $$t_d(1\to2)=1.0\text{ h},\ \ t_d(2\to4)=1.0\text{ h},\ \ t_d(4\to8)=1.1\text{ h},\ \ t_d(8\to12)=1.1\text{ h}.$$ The near-constant $\sim\boxed{1.05\ \text{h}}$ doubling time over 11 h and a rise of more than three orders of magnitude is the signature of true exponential growth.
3. Stationary phase, 12–20 h. Doubling time lengthens sharply ($t_d(12\to16)=5.4$ h, $t_d(16\to20)=4.0$ h) as growth decelerates and the population approaches its peak of $4(10^9)$/mL at $t=20$ h — net growth rate is falling toward zero as births are increasingly offset by deaths.
4. Death (decline) phase, 20–28 h. Count falls by more than two orders of magnitude, from $4(10^9)$/mL at 20 h to $1(10^7)$/mL at 28 h, as the death rate now exceeds any residual growth.

(ii) Major events per phase

Lag: no increase in cell numbers; cells are synthesizing the enzymes and cofactors needed for growth in the new medium and adapting metabolically, without yet dividing. Exponential (log): cells divide by binary fission at the fastest, most uniform rate the medium/temperature allow, with a constant doubling time; this is the period of greatest metabolic uniformity and the phase most sensitive to environmental and chemical stress. Stationary: net growth rate falls to zero as the rate of new cell division is balanced by the rate of cell death, driven by nutrient depletion, accumulation of inhibitory metabolic byproducts, and/or reduced available oxygen. Death: the death rate now exceeds any residual division rate and viable count declines, often following its own exponential (first-order) decay as cells lyse or become non-culturable.

(iii) Phase most susceptible to metabolic inhibitors

The exponential (log) phase. Metabolic inhibitors (most antibiotics and many sanitizers) act by disrupting active processes — cell-wall synthesis, protein synthesis, DNA replication — that are running at their maximum rate only while cells are actively dividing. Lag-phase and stationary/death-phase cells have much lower biosynthetic activity and are correspondingly far more tolerant of such inhibitors.

(iv) Two factors terminating the log phase

(1) Nutrient depletion — the limiting substrate (carbon/energy source, nitrogen, or a specific micronutrient) falls to a concentration that can no longer support the maximum growth rate; and (2) accumulation of inhibitory metabolic byproducts (organic acids, ethanol, or other waste metabolites, and the associated pH shift) that increasingly suppress further division as their concentration builds up.