Question

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.

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

For bacterial growth, use exponential growth models, which show a rapid increase initially followed by leveling off as resources become limiting.

Answer 1

The Correct Option is A

To determine the optimal graph for depicting bacterial colony growth, it is necessary to examine the governing principles of bacterial proliferation:

In a simplified form, the quantity of bacteria \( N \) at a given time \( t \) can be quantified as \( N(t) = N_0 \times e^{kt} \). Here, \( N_0 \) signifies the initial bacterial count, and \( k \) represents the constant growth rate. This mathematical expression aligns with the exponential growth model, analogous to the principles observed in radioactive decay.

An exponential growth model of this nature is most effectively visualized through a graph characterized by:

• The vertical axis (y-axis), representing the bacterial population, \( N(t) \).
• The horizontal axis (x-axis), denoting the passage of time, \( t \).
• A curved line illustrating a steepening rate of increase as time advances.

The representation of the appropriate graph among the available selections is as follows:

This particular graph exhibits an exponential curve, a characteristic signature of bacterial growth over time, assuming an environment with abundant resources.

Consequently, this graph accurately portrays bacterial colony expansion governed by exponential growth dynamics, comparable to radioactive decay. The bacterial population experiences an exponential surge with increasing time.