A bacterial culture undergoing balanced growth requires a first-order reaction. In other words, the rate of increase in bacteria at any particular time is proportional to the number or mass of bacteria present at that time. If 'N' is the number of cells at any given time 't and 'μ' is "growth rate constant" this process can be expressed mathematically as
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\(\rm \frac{dN}{dt}=\mu N\)
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\(\rm \frac{dt}{dN}=\mu N\)
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\(\rm \frac{d\mu}{dt}= N\)
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\(\rm \frac{dN}{dt}\times N=\mu \)