Generation Time of Bacteria Calculator

The exponential growth of bacteria is calculated using the following formula:

\[ N(t) = N(0) \cdot (1 + r)^t \]

Where:

\( N(t) \) = Population at time \( t \)

\( N(0) \) = Initial number of bacteria

\( r \) = Growth rate

\( t \) = Elapsed time

To calculate the bacterial growth rate \( r \), we rearrange the formula:

\[ r = \left( \frac{N(t)}{N(0)} \right)^{\frac{1}{t}} - 1 \]

The doubling time \( t_d \) is calculated as:

\[ t_d = \frac{\ln(2)}{\ln(1 + r)} = t \cdot \frac{\ln(2)}{\ln\left( \frac{N(t)}{N(0)} \right)} \]

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