Calculadora de Previsão por Crescimento Exponencial
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
y(t) = y₀ · e^(r·t)
About this calculator
This calculator projects a future value using the continuous exponential growth model. The formula y(t) = y₀ · e^(r·t) describes how a quantity grows at a constant relative rate r over time t, starting from an initial value y₀. This model is widely used in finance, biology, and demography to simulate phenomena that multiply rapidly.
It works simply: you enter the initial value, the growth rate (as a percentage), and the time period. The calculator applies the exponential formula, converting the percentage rate to decimal and using Euler's number (e ≈ 2.71828). The result shows the projected value after the specified time, assuming continuous, uninterrupted growth.
Use this calculator to estimate future populations, continuous compound interest projections, bacterial growth in labs, or asset appreciation at a constant rate. It is ideal for scenarios where growth is continuous rather than discrete, such as in theoretical mathematical models.
Caution: the model assumes a constant growth rate r, which rarely holds in practice. For long periods, small rate variations lead to large differences. Also, the formula ignores environmental or capacity limits, as in real populations. Use with care for long-term forecasts.
Frequently asked questions
What is the difference between exponential and linear growth?
In linear growth, the quantity increases by a fixed amount each period. In exponential growth, the increase is proportional to the current value, causing acceleration over time.
Can I use this calculator for compound interest?
Yes, but only for continuous compounding. For discrete compounding (monthly, yearly), other formulas are more appropriate.
What does a negative growth rate mean?
A negative rate indicates exponential decay, such as in radioactive decay or asset depreciation. The formula still works, resulting in decreasing values.
How do I convert a percentage rate to decimal?
Divide the percentage value by 100. For example, 5% becomes 0.05. The calculator does this automatically.
Is the result accurate for long-term forecasts?
Accuracy depends on the rate remaining constant. For long periods, small rate variations cause large deviations. The model is more reliable for short periods or when the rate is stable.