anonymous
  • anonymous
The amount of carbon 14 remaining in a sample that originally contained A grams is given by C(t) = A(0.999879)t where t is time in years. If tests on a fossilized skull reveal that 99.89% of the carbon 14 has decayed, how old, to the nearest 1,000 years, is the skull?
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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campbell_st
  • campbell_st
so the initial value of A is 100 C(t) = 100 - 99.89 so C(t) = 0.11 using the formula \[0.11 =100(0.999879)^t\] divide both side by 100 \[0.0011 = (0.999879)^t\] take the log of both sides \[\ln(0.0011) = t \times \ln(0.999879)\] making t the subject \[t = \frac{\ln(0.0011)}{\ln(0.999879)}\]
campbell_st
  • campbell_st
C(t) = 0.11 is the amount of carbon 14 left in the scull, as a percentage

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