This tool simulates the exponential growth of a bacterial population using the classic Malthusian model. It allows users to explore how initial population size and growth rate affect bacterial proliferation over time.
Users specify the initial population (N₀), growth rate (r), simulation duration (t_max), and resolution parameters. The tool computes population dynamics and visualizes results through multiple professional representations.
The underlying model is continuous exponential growth:
\[ N(t) = N_0 e^{rt} \]
where: - \( N(t) \) is the population at time t - \( N_0 \) is the initial population - \( r \) is the intrinsic growth rate (per unit time) - \( t \) is time
The doubling time, when population doubles, is given by:
\[ t_d = \frac{\ln 2}{r} \]
For parametric analysis, the tool generates a 3D surface of final population over variations in N₀ and r:
\[ N(t_{\text{max}}) = N_0 e^{r t_{\text{max}}} \]
Overflow protection handles extremely large populations by capping values when numerical limits are exceeded.
The tool provides various visualizations including static multi-curve plots (log scale), interactive 2D curves, 3D population surfaces, manual/animated 3D evolution, classic growth curves with annotations, and engaging animated representations of bacterial multiplication (swarm and individual cell appearance).
Ideal for studying microbial kinetics, understanding exponential processes, analyzing growth phases, teaching population dynamics, and exploring biological amplification in microbiology and biotechnology.
