# Generation Number Calculator

## What is Generation Number?

The generation number refers to the number of generations it takes for a population to reach a certain size from an initial population size, assuming exponential growth.

The equation for calculating the generation number is derived from the exponential growth equation and the concept of the logarithm. It is given by:

Generation Number = (log(populationT) - log(population0)) / 0.301

Where:

• populationT represents the population size at time "t".
• population0 represents the initial population size.

In the equation, the logarithm base is typically 10, which means the logarithms are calculated using base-10 logarithms. The constant value of 0.301 is the approximate logarithm of 2 with a base of 10 (log10(2)).

By taking the logarithm of the population sizes and dividing their difference by the logarithm of 2, we can determine the number of times the population has doubled or increased by a factor of 2. Dividing this value by the generation time (the time it takes for a generation to pass) gives us the generation number.