anonymous
  • anonymous
the half-life of a radioactive element is 138 days, but your sample will not be useful to you after 60% of the radioactive nuclei originally present have disintegrated. about how many days can you use the sample? a. 187 b. 167 c. 172 d. 182
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
182
anonymous
  • anonymous
\[138 \times 1/(2^{x}) =138 \times 40% \] \[2^{x} = 100/40\] \[x = \log_{2} (5/2)\]\[x = 1.321928\] if x = 1, then x = 138 days, in this case x = 1.321928, so duration : 138 x 1.321928 = 182.43324
anonymous
  • anonymous
\[(\frac{1}{2})^{\frac{t}{138}}=.6\] \[\frac{t}{138}=\frac{\ln(.6)}{\ln(.5)}\] \[t=\frac{138\ln(.6)}{\ln(.5)}\]

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anonymous
  • anonymous
oops no that is wrong. after 60% is gone only 40% remains, so should have written \[t=\frac{138\ln(.4)}{\ln(.5)}\]
anonymous
  • anonymous
Cool how to use that ln?

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