For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the followi

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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 -…

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Given: Bacterial growth is stated to follow a law similar in form to radioactive decay, but for growth the number increases with time.

Find: Which graph best represents bacterial colony growth.

For bacterial growth, the number of bacteria at time $t$ is given by

N(t) = N_0 e^{kt}

where $N_0$ is the initial number of bacteria and $k$ is the growth constant.

So,

\frac{N}{N_0} = e^{kt}

This means $N/N_0$ increases exponentially with time.

Therefore, the correct graph must show an upward-curving exponential increase as time increases.

The selected graph shows $$N/N_0$$ on the vertical axis and time on the horizontal axis, with an exponentially increasing curve.

Thus, the correct option is A.

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