Algebra Notes

Algebra Notes - Every radioactive element has a half-life...

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Section 5.6 Applications of Exponential and Logarithmic Functions Objective 1: Solving Compound Interest Applications 5.6.2 How long (in years and months) will it take for an investment to double if it is invested at 8% compounded monthly? 5.6.3 How long will it take for an investment to triple if it is compounded continuously at 4%? (two decimal places) Objective 2: Exponential Growth and Decay Applications 5.6.6 The population of Adamsville grew from 6000 to 13,000 in 8 years. Assuming uninhibited exponential growth, what is the expected population in an additional 3 years?
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0 ( ) kt A t A e = ( 29 0 0, A Exponential Decay A model that describes the exponential decay of a population, quantity or amount A , after a certain time, t, is 0 ( ) kt A t A e = where 0 (0) A A = is the initial quantity and 0 k < is a constant called the relative decay constant . (Note: k is sometimes given as a percent.) Half-Life:
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Unformatted text preview: Every radioactive element has a half-life, which is the required time for a given quantity of that element to decay to half of its original mass. 5.6.10 A certain radioactive isotope has leaked into a small stream. On hundred days after the leak, 12% of the original amount of the substance remained. Determine the half-life of the radioactive isotope. 5.6.12 A superhero is rendered powerless when exposed to 60 or more grams of a certain element. A 650-year-old rock that originally contained 400 grams of this element was recently stolen from a rock museum by the superhero’s nemesis. The half-life of the element is known to be 250 years. a) How many grams of the element are still contained in the stolen rock? b) For how many years can this rock be used by the superhero’s nemesis to render the superhero powerless?...
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Algebra Notes - Every radioactive element has a half-life...

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