N(t) = N₀ × e^(−λt) | A = λN
Radioactive decay follows first-order kinetics: N(t) = N₀e^(−λt), where λ = ln(2)/t½ is the decay constant. Activity A = λN = A₀e^(−λt), measured in becquerels (1 Bq = 1 decay/s) or curies (1 Ci = 3.7 × 10¹⁰ Bq). Types of decay: alpha (⁴He²⁺ emission), beta-minus (neutron → proton + electron), beta-plus/EC (proton → neutron + positron), and gamma (electromagnetic radiation). Applications: carbon-14 dating (archaeology, up to ~50,000 years), medical imaging (⁹⁹ᵐTc, t½ = 6 h), cancer treatment (⁶⁰Co, ¹³¹I), nuclear power, smoke detectors (²⁴¹Am), and geological dating (K-Ar, U-Pb methods for billions of years).