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
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 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 Interest | Growth | A = P(1 + r/n)^(nt) | Bank savings, investments |
| Population Growth | Growth | P(t) = P₀e^(rt) | Bacteria, human populations |
| Radioactive Decay | Decay | N(t) = N₀e^(-λt) | Carbon dating, nuclear physics |
| Depreciation | Decay | V(t) = V₀(1 - r)^t | Car value, equipment |
| Inflation | Growth | P(t) = P₀(1 + r)^t | Price 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.