Section10_4_review - Section 10.4 Exponential Growth and...

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Section 10.4: Exponential Growth and Decay Exponential growth and decay problems are problems involving: Population growth Radioactive decay Continuous compounding of interest (money in an account in which the compounding is continuous) Exponential growth and decay problems are governed by the equation A = A 0 e kt where, A 0 = initial quantity A = final quantity t = time k = constant which is unique to the problem (For continuous compounding of interest problems, k is the interest rate expressed as a decimal.) Note that: k 0 is for exponential growth, and k < 0 is for exponential decay. Problem. Carbon 14, with a half-life of 5700 years, is used to estimate the age of organic materials. What fraction of the original amount of carbon 14 would an object have if it were 2000 years old? Solution. A = A 0 e kt Step 1 – determine k from half-life information. 1 2 A 0 = A 0 e k 5700 ( 29 1 2 = e 5700 k ln 1 2 = ln e 5700 k = 5700 k k = ln 1 2 5700 = ln1 - ln 2 5700 = 0 - ln2 5700 = - ln 2 5700 Step 2 – determine the fraction of the original amount of carbon 14 remaining after 2000 years.
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