Exponential growth and decay

Math

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

  • A population of bacteria doubling every hour: P(t) = P₀ · 2ᵗ
  • Radioactive decay with a half-life of 5 years
  • 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)

Related Terms

Exponential models Natural log Solving exponential equations Logarithm properties

Study This Concept

Practice exponential growth and decay with free review games in these units:

Algebra 2 Unit 7: Exponential and Logarithmic Functions