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. How old, to the nearest 1,000 years, is a fossil in which only 30% of the carbon 14 has decayed?

Question

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. How old, to the nearest 1,000 years, is a fossil in which only 30% of the carbon 14 has decayed?

anonymous · Answer

The equation should be C(t) = A(0.999879^t)

39% = 100% * (0.999879^t)

0.999879^t = 0.39
t log0.999879 = log0.39
t = log0.39/log0.999879
t = 7781 = 8000 years

So your answer would be "8000 years"