Calculate the future value of a quantity that grows or shrinks at a constant percentage rate over time.
Exponential growth happens when a quantity increases by a fixed percentage each period (like compound interest or population growth). Exponential decay is the opposite — a fixed percentage decrease each period (like radioactive decay or depreciation).
Growth: Final Value = Initial × (1 + rate)^periods
Decay: Final Value = Initial × (1 - rate)^periods
A population of 1,000 growing at 5% per year for 10 years reaches 1,000 × (1.05)^10 ≈ 1,629 — a total increase of about 62.9%.
Using the formula N = N0 × e^(rt) for continuous growth, or N = N0 × (1+r)^t for discrete periodic growth, where N0 is the starting value, r is the growth rate, and t is time.
A positive rate (r > 0) produces growth (increasing values over time); a negative rate (r < 0) produces decay (decreasing values over time).
Compound interest, population growth under unlimited resources, and viral spread in early stages are classic examples of exponential growth patterns.