Exponential Growth & Decay

AP Calculus · Axiom Academy

Lesson Exponential Growth & Decay The most important differential equation in science Exponential Growth/Decay Model k > 0 : exponential growth. k < 0 : exponential decay. This comes directly from separation of variables: . Radioactive decay: Half-life T_ 1/2 means Population growth: A colony starts at 100 and doubles every 3 hours. Then and . Continuously compounded interest: A = Pe^ rt where r is the annual rate. Newton s Law of Cooling: with solution T(t) = T_s + (T_0 - T_s)e^ kt

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