Exponential Functions and Growth/Decay

SAT Math · Axiom Academy

Exponential Functions: Growth & Decay Model Real-World Situations with Exponentials The Exponential Function Formula An exponential function models quantities that grow or decay by a constant percent rate. t = time (often in years, but depends on the problem) How to Read the Growth Factor b: If → growth (population increasing, value rising) If → decay (half-life, depreciation) If something grows by r% per year , then If something decays by r% per year , then Graph: Curves upward, gets steeper Graph: Curves downward, approaches 0 Two special concepts the SAT loves: Time it takes for a quantity to reduce to half its value. Carbon-14 has a half-life of 5,730 years. If a sample starts with 100g, how much remains after 11,460 years? Time it takes for a quantity to double . General Doubling Time Formula: where DT = doubling time period A population of bacteria doubles every 3 hours. Starting with 1,000, how many are there after 12 hours? A city has 50,000 residents and grows at 3% per year. Write an equation and find the population in 10 years. A radioactive element decays at 15% per year. If you start with 200g, write an equation and find the amount after 5 years. 3. Compound Interest (Continuous) 4. Compound Interest (Regular) Read the problem carefully: Is it growth or decay? Identify: initial amount (a), growth/decay rate (r) Calculate b = 1 + r (growth) or b = 1 - r (decay)

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