Exponential Growth & Decay Calculator
Calculate exponential growth, decay, half-life, and Newton's cooling.
Population Growth
Radioactive Decay
Half-Life
Newton\'s Cooling
Result
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Enter parameters and calculate
Final Amount
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Growth Factor
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Doubling Time
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Half-Life
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Exponential Models
Growth & Decay Formula
P(t) = P₀ × e^(rt)
r > 0 for growth, r < 0 for decay
Half-Life Formula
N(t) = N₀ × (1/2)^(t/T)
T = half-life period
Newton's Law of Cooling
T(t) = Tₐ + (T₀ - Tₐ)e^(-kt)
Common Applications
| Application | Model | Example |
|---|---|---|
| Population | Growth | Demographics |
| Radioactive | Decay | Carbon dating |
| Bacteria | Growth | Lab cultures |
| Drug elimination | Decay | Pharmacology |
| Cooling object | Cooling | Forensics |
Half-Life Examples
- Carbon-14: 5,730 years
- Uranium-238: 4.5 billion years
- Iodine-131: 8 days
- Caffeine: ~5 hours
Frequently Asked Questions
What is the relationship between half-life and decay constant?
Half-life T = ln(2)/λ or λ = ln(2)/T. The decay constant is the inverse of half-life scaled by ln(2).
How do I find doubling time?
Doubling time = ln(2)/r where r is the growth rate. For 5% annual growth, doubling time ≈ 13.9 years.