Math
Exponential growth and decay.
Definition
Exponential growth occurs when a quantity increases by a constant percentage over equal time intervals, while exponential decay occurs when it decreases by a constant percentage. Both are modeled by exponential functions.
Examples
Real-world.
- 1 A population of bacteria doubling every hour: P(t) = P₀ · 2ᵗ
- 2 Radioactive decay with a half-life of 5 years
- 3 A car losing 15% of its value each year
Key Fact
Growth: y = a(1+r)ᵗ; Decay: y = a(1-r)ᵗ; Continuous: y = ae^(kt)