Exponential Growth Calculator

Calculate exponential growth and decay with compound interest, population growth, and radioactive decay models. Perfect for finance, biology, and physics applications.

Exponential Growth & Decay Calculator


Select a growth type to see the formula

Growth & Decay Examples

Click on these links to see instant calculations with common scenarios:

Exponential Growth & Decay

Exponential growth and decay describe processes where quantities change at rates proportional to their current values. These models are fundamental in finance, biology, physics, and many other fields.

Growth & Decay Formulas

Exponential Growth: A = P(1 + r)^t
Exponential Decay: A = P(1 - r)^t
Compound Interest: A = P(1 + r/n)^(nt)
Continuous Growth: A = Pe^(rt)

Where:
• A = Final amount
• P = Initial amount (principal)
• r = Growth/decay rate (as decimal)
• t = Time
• n = Compounding frequency
• e ≈ 2.71828 (Euler's number)

Common Applications

Application Type Formula Example
Compound InterestGrowthA = P(1 + r/n)^(nt)Bank savings, investments
Population GrowthGrowthP(t) = P₀e^(rt)Bacteria, human populations
Radioactive DecayDecayN(t) = N₀e^(-λt)Carbon dating, nuclear physics
DepreciationDecayV(t) = V₀(1 - r)^tCar value, equipment
InflationGrowthP(t) = P₀(1 + r)^tPrice increases over time
  • Finance: Calculate compound interest, investment growth, and loan calculations
  • Biology: Model population growth, bacterial cultures, and ecological systems
  • Physics: Analyze radioactive decay, cooling processes, and exponential phenomena
  • Economics: Study inflation, economic growth, and market trends
  • Engineering: Design systems with exponential behavior and decay processes

Frequently Asked Questions

What is exponential growth?

Exponential growth occurs when a quantity increases at a rate proportional to its current value, following the formula A = P(1 + r)^t where A is final amount, P is initial amount, r is growth rate, and t is time.

How do you calculate compound interest?

Compound interest is calculated using A = P(1 + r/n)^(nt) where P is principal, r is annual interest rate, n is compounding frequency, and t is time in years.

What is exponential decay?

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, following the formula A = P(1 - r)^t or A = Pe^(-kt) for continuous decay.

See Also