Calculadora de Constante de Taxa de Crescimento
Calcule a constante de taxa de crescimento de populações celulares ou bacterianas.
Specific Growth Rate (k)
0.0866 1/h
Specific Growth Rate (k) vs Doubling Time (td)
Formula
## Exponential Growth Prediction With a known growth rate, you can predict future population sizes during exponential growth. ### Formulas **k = ln(2) / td** (growth rate from doubling time) **N(t) = N0 × e^(kt)** (population at time t) These predictions are valid only during log-phase growth. In reality, nutrients become limiting and growth slows as the population approaches carrying capacity.
Exemplo Resolvido
Starting with 1000 cells, doubling time 8 hours, predict at 48 hours.
- 01k = ln(2) / 8 = 0.0866 h⁻¹
- 02Generations = 48 / 8 = 6.0
- 03N(48) = 1000 × e^(0.0866 × 48) = 1000 × e^4.159 = 1000 × 64 = 64,000 cells
Perguntas Frequentes
How long does exponential growth last?
Exponential growth continues until nutrients are depleted, waste products accumulate, or space runs out. For bacteria in rich media, this may be 4-8 hours. For mammalian cells, confluence is reached in 3-5 days.
What is the carrying capacity?
Carrying capacity K is the maximum sustainable population. Growth follows a logistic curve: dN/dt = kN(1-N/K). As N approaches K, growth slows to zero. This model is more realistic than pure exponential.
Can I use this for bacterial culture scale-up?
For initial planning, yes. Use the exponential model to estimate when a culture will reach a target density. In practice, monitor OD and adjust for lag phase and nutrient limitations.
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