Continuous Decay
P = P₀ × e^(-r × t)
Used for radioactive decay, natural processes
Discrete Decay
P = P₀ × (1 - r/n)^(n × t)
Used for depreciation, periodic decay
P = Final value after decay
P₀ = Initial value
r = Decay rate (as decimal)
t = Time period
n = Compounding periods per year
e = Euler's number (~2.71828)
Radioactive Decay
Half-life of isotopes, nuclear physics
Asset Depreciation
Vehicle, equipment, property value loss
Population Decline
Species extinction, disease decay
Drug Metabolism
Medicine half-life in the body
Exponential decay is a mathematical concept that describes how quantities decrease at a rate proportional to their current value. Unlike linear decay where values decrease by a fixed amount, exponential decay means the rate of decrease slows down over time as the quantity gets smaller. This pattern is observed in many natural and economic phenomena.
The key characteristic of exponential decay is the concept of "half-life" - the time it takes for a quantity to reduce to half its original value. This half-life remains constant regardless of the starting amount, making exponential decay predictable and widely applicable in fields ranging from nuclear physics to finance and pharmacology.
Enter your initial value (the starting amount), decay rate (as a percentage), and time period in years. Choose between continuous decay (for natural processes like radioactive decay) or discrete compounding frequencies (for financial depreciation). The calculator will show the final value, total decrease, and a year-by-year breakdown of the decay process.
Disclaimer: Exponential decay calculations are based on standard mathematical formulas. Results may vary due to rounding and compounding assumptions. For scientific applications, consult with domain experts and use specialized software for precise calculations.