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Compute N_t = N₀·e^(rt) with fold change, doublings, doubling time, or half-life.
Execution
Fill in the form, run the tool, and review the result in one place.
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Tool usage guide
Compute future population size with the continuous exponential model N_t = N₀ · e^(rt). Enter starting size, constant per-capita rate r and elapsed time t (same units) to obtain N_t, fold change, number of doublings, and either doubling time (r > 0) or half-life (r < 0). The calculator is intended for unlimited-resource phases such as bacterial log growth.
Background
An early log-phase culture is started with 1 000 cells that grow at a constant rate of 0.4 h⁻¹.
Problem
Predict the cell count after 10 hours and obtain the corresponding fold change, number of doublings and doubling time.
How to use
Enter N₀ = 1000, r = 0.4, t = 10 and leave decimal places at the default of 2.
Outcome
The culture reaches 54 598.15 cells (fold change ×54.60, 5.77 doublings, doubling time 1.73 h).
Background
A population of 100 000 individuals is declining at a constant rate of −0.1 per time unit.
Problem
Estimate remaining numbers after 20 time units and obtain the half-life.
How to use
Enter N₀ = 100000, r = −0.1, t = 20.
Outcome
The population falls to 13 533.53 (fold change ×0.1353, half-life 6.93 time units).
N_t = N₀ · e^(rt), the standard continuous exponential-growth equation.
Yes. Both must be expressed in identical units (hours, days, etc.).
The population declines exponentially; the calculator reports half-life instead of doubling time.
Fold change equals e^(rt); the number of doublings is rt / ln(2).
When resources become limiting or the population approaches carrying capacity; a logistic model is then more appropriate.