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exp growth_decay

For the same town how many years will it take for the

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Unformatted text preview: For the same town, how many years will it take for the population to double in size? Solution: We wish to find t when y ( t ) = 2 y . y ( t ) = 10000(1 . 1) t/ 2 20000 = 10000(1 . 1) t/ 2 2 = 1 . 1 t/ 2 ln2 = ln 1 . 1 t/ 2 = t 2 (ln1 . 1) t = 2ln2 ln1 . 1 ≈ 14 . 55 yrs Example 2a Radioactive Decay. Find rate constant k given a fraction (or percentage) of y at time t . The rate at which a radioactive element decays is approximately proportional to the number of radioactive nuclei present. A radioactive element’s half-life is the time required for half of the nuclei to decay. Radioactive carbon-14 has a half-life of 5700 years. Find the relative growth rate k . Solution: We wish to find the carbon-14 rate constant given y (5700) = y / 2 . y ( t ) = y e kt y (5700) = y e k (5700) y 2 = y e 5700 k 1 2 = e 5700 k ln 1 2 = ln e 5700 k = 5700 k k = ln 1 2 5700 =- ln2 5700 (Note that ln 1 2 = ln2 (- 1) =- ln2 .) Example 2b Find time t given k and a fraction (or percentage) of y . A fossilized animal bone contains 30% of its original carbon-14 content. Approximately how many years ago did the animal die?...
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