🧫 Microbiology & Cell Culture Kinetics
Bacterial Exponential Growth & Doubling Calculator
Compute final bacterial colony population ($N(t) = N_0 \cdot 2^n = N_0 \cdot e^{\mu t}$), generation count ($n$), specific growth rate ($\mu$), and doubling time ($t_d$).
🦠 E. coli ($t_d = 20\text{ min}$)
🧫 S. aureus ($t_d = 30\text{ min}$)
🍞 Yeast ($t_d = 90\text{ min}$)
🩺 M. tuberculosis ($t_d = 18\text{ hr}$)
Growth Parameters
Final Population Count (N_t)
409,600 Cells (CFU)
Generations ($n$)
12.0
Specific Rate ($\mu$)
2.079 / hr
Log₁₀ Increase
+3.61 Log CFU
💡 Exponential Growth Formula:
$$N_t = N_0 \times 2^n = 100 \times 2^{12} = 100 \times 4096 = 409,600\text{ cells}$$
Microbial Growth Kinetics
During logarithmic (exponential) growth phase, single-cell binary fission follows:
- Population Growth: $$N(t) = N_0 \cdot 2^n = N_0 \cdot e^{\mu t}$$
- Number of Generations ($n$): $$n = \frac{t}{t_d} = \frac{\log_{10}(N_t) - \log_{10}(N_0)}{\log_{10}(2)}$$
- Specific Growth Rate ($\mu$): $$\mu = \frac{\ln(2)}{t_d} \approx \frac{0.69315}{t_d}$$