For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth? Where N – Number of Bacteria at any time, – Initial number of Bacter

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Solution

Q.
For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth

Where N – Number of Bacteria at any time, $N_{0}$ – Initial number of Bacteria. [2025]

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Ans.
(1)

Initial number of bacteria = $N_{0}$

Number of bacteria at time t = N

Rate of increase of bacteria = $\frac{d N}{d t}$

As bacteria grow by first order:

$\frac{d N}{d t} = k N$

$\frac{d N}{N} = k dt$

Integrate both sides:

$\int_{N_{0}}^{N} \frac{d N}{N} = \int_{0}^{t} k dt$

${[\ln N]}_{N_{0}}^{N} = k {[t]}_{0}^{t}$

$N = N_{0} e^{k t}$

This is exponential growth.

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