anonymous
  • anonymous
the half-life of carbon-14 is 5700 years. find the age of a sample at which 9% of the radioactive nuclei originally present have decayed? a. 1776 years b. 676 years c. 1226 years d. 776 years
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
This can be solved as a ratio, can't it? \[{50/100 \over 5700} = {9/100 \over x}\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
It's a differential equation problem. This is kind of a classic differential equation which has the solution x(t) = e^(-k * t) * e^c x(t) is the amount of carbon 14 left after t years. e^c is the initial amount of carbon 14 (put in t=0 to see this). x(5700) = 1/2 * e^c. Some algebra gives you k = ln(2^(1/5700)) now to find the time that gives you 9% loss of carbon: x(t) = 0.91 * e^c some algebra gives you t = ln(1/(0.91^(1/ln(2^(1/5700))))) This comes out as 775.551... So after 776 years 9% will have decayed.

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