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anonymous
 4 years ago
An isotope has a halflife of 5,000 years, How long will it take to decay to 15% of its original quantity?
anonymous
 4 years ago
An isotope has a halflife of 5,000 years, How long will it take to decay to 15% of its original quantity?

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Rogue
 4 years ago
Best ResponseYou've already chosen the best response.1\[f(t) = Ae ^{kt}\]\[k = \frac {ln 2}{t _{\frac{1}{2}}} = \frac {ln 2}{5000} = 0.000138629436 \]We'll let A = 100, so its easy to see the percent change.\[f(t) = 100e^{0.000138629436t} = 15\]\[.15 = e^{0.000138629436t}\]\[t = \frac {\ln .15}{0.000138629436} \approx 13685 years\]

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.1The constant is negative in the exponential decay equation, I made a mistake when I first wrote the equation. \[f(t) = Ae^{kt}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay thank you. may i ask though how you found k?

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.1Exponential decay is first order, so there is a formula that relates the half life and the constant.\[t _{\frac{1}{2}}^{} = \frac {\ln 2}{k}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay, thank you very much!

Rogue
 4 years ago
Best ResponseYou've already chosen the best response.1Alright, no problem, good luck with your studies :)
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