Generation Time Calculator
Doubling time (Td): Not calculated yet
Exponential growths model many phenomena, from biology to finance: with this bacterial generation time calculator you will discover how to calculate bacterial growth over time, its main features, and parameters. Here you’ll learn:
- The rules of bacterial population growth;
- How to calculate the bacterial growth rate; and
- What is generation time of bacteria populations.
If you want to find out more about bacterial population growth, why it is important, and about an interesting bacterial experiment, then keep on reading!
What is exponential growth?
Exponential growth models are used when a quantity, a function, or, in our case, the size of a bacteria population increases over time by a constant percent increase per time unit, with the size of the increment depending on the value of the function at the last step. This form of bacterial growth is essential to the modern world, including the cleaning water in a wastewater plant!
Exponential growth models often describe functions with “lazy” beginnings followed by explosive increases; exponentials are, in fact, the fastest-growing functions in mathematics.
We got a taste of exponential growth during the coronavirus pandemic: a few cases one day, a little bit more the day after, and then things went out of control: without precautions, the initial phases of an epidemic follows the exponential — then, luckily it slows down.
How do we calculate the generation time of bacteria?
The equation that controls the exponential growth is:
where:
Often, the time �0t0 is set to 00, which simplifies the equation to:
�(�)=�(0)⋅(1+�)�N(t)=N(0)⋅(1+r)t
This is how to calculate the bacterial growth rate, �r, we rearrange the formula:
�=�(�)�(0)1�−1r=N(0)N(t)t1−1
What is generation time?
A commonly used quantity in the study of populations is the generation time, ��td, that is, the required time for the population to double in size through binary fission:
The doubling time is:
�d=ln(2)ln(1+�)=�⋅ln(2)ln(�(�)�(0))td=ln(1+r)ln(2)=t⋅ln(N(0)N(t))ln(2)