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