Continuous Growth
P = P₀ × e^(r × t)
Discrete Compounding
P = P₀ × (1 + r/n)^(n × t)
P₀ = Initial value
r = Growth rate (as decimal)
t = Time in years
n = Compounding periods per year
e = Euler's number (~2.71828)
Population Growth: Modeling bacteria, human populations
Compound Interest: Investment returns, savings accounts
Radioactive Decay: Half-life calculations (negative rate)
Technology: Moore's Law, viral spread
Exponential growth occurs when a quantity increases at a rate proportional to its current value. Unlike linear growth, where a constant amount is added over time, exponential growth multiplies by a constant factor. This leads to increasingly rapid growth as time progresses, creating the characteristic "J-shaped" curve.
The key feature of exponential growth is that the rate of change is always proportional to the current size. For example, if a population doubles every year, it will grow from 100 to 200 in year one, 200 to 400 in year two, and 400 to 800 in year three - the absolute increase gets larger each period even though the percentage increase stays constant.
Enter your initial value (the starting amount), growth rate (as a percentage), and time period (in years). Select the compounding frequency that matches your scenario - continuous compounding is often used for natural phenomena and theoretical calculations, while discrete compounding (yearly, monthly, etc.) is more common for financial applications.
For decay scenarios (like radioactive decay or depreciation), enter a negative growth rate. The calculator will show how the value decreases over time using the same exponential formula.
Disclaimer: Exponential growth calculations are based on standard mathematical formulas. Results may vary due to rounding and compounding assumptions. Real-world growth patterns may deviate from pure exponential models due to limiting factors and external influences.