Exponential Functions

Question

1. Scientists have observed that living matter contains, in addition to carbon, C 12, a fixed Percentage of a radioactive isotope of carbon, C14. When the living material dies, the amount of C12 present remains constant, but the amount of C14 decreases exponentially with a half life of 5,550 years. In 1965 the charcoal from cooking pits found at a site in Newfoundland used by Vikings was analyzed, and the percentage of C14 remaining was found to be 88.6%. What was the approximate date of this Viking settlement ?

Answer 1

A = a₀(0.5)^t/h

0.886a₀ = a₀(0.5)^t/5550         substitution

0.886 = (0.5)^t/5550                divide both sides by a₀

ln 0.886 = ln (0.5)^t/5550

-0.1210 ≈ (t/5550)(-0.6931)

-671.76 ≈ -0.6931t

721.55 ≈ t

 

The approximate date of the settlement was 1965 - 721.55, or 1243.