Exponential Growth & Decay Calculator
How It Works
This exponential growth & decay calculator uses established formulas to provide accurate results.
The basic rule:
- A = P(1 + r)^t (growth)
- A = P(1 - r)^t (decay)
- Doubling time = ln(2) / ln(1 + r)
- Half-life = ln(0.5) / ln(1 - r)
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is exponential growth?
Exponential growth occurs when a quantity increases by a fixed percentage each period. The formula is A = P(1+r)^t, where P is the initial amount, r is the rate per period, and t is the number of periods.
What is the doubling time?
Doubling time is how long it takes for a quantity to double. It equals ln(2)/ln(1+r). The Rule of 72 approximation says doubling time ≈ 72/(rate%), which works well for small rates.
What is half-life?
Half-life is the time it takes for a decaying quantity to reduce to half its value. It equals ln(0.5)/ln(1-r). This concept is central to radioactive decay, pharmacology, and depreciation.
What is the difference between exponential and linear growth?
Linear growth adds a fixed amount each period (e.g., +100/year). Exponential growth multiplies by a fixed factor each period (e.g., ×1.05/year). Exponential growth starts slowly but eventually outpaces any linear growth.