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Cyberpunk Math Lab: The Non-Linear World FREE
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Exponential Growth & Decay
Learning Objectives
- Model exponential situations
- Distinguish growth from decay
- Calculate future values
Key Concepts
Exponential Growth
y = a(1 + r)ᵗ where r > 0
Exponential Decay
y = a(1 - r)ᵗ where 0 < r < 1
Theory
**General form:** y = a · bᵗ
- a = initial amount
- b = growth factor (b > 1 = growth, 0 < b < 1 = decay)
- t = time
**Growth:** y = a(1 + r)ᵗ (r = rate as decimal)
**Decay:** y = a(1 - r)ᵗ
**Half-life:** Time for quantity to halve. After n half-lives: y = a(½)ⁿ
Examples
$1000 at 5% annual growth for 3 years
Solution: 1000(1.05)³ = $1157.63