For the decomposition of Carbon 14, find the age of a prehistoric cave painting discovered in the Lascaux Caves in southern France if the amount of Carbon 14 has decayed to 14.29%...again using calculus formulas. Not sure how to use this equation (content section of course never gave a proper example): C(t) = C0e-0.0001216t. Thanks.
2 answers
I figured out e but I am confused for the rest of the equation.
You can figure out the age by either using the 1/e "decay constant" or the half life. The half life of C-14 is 5568 years, according to my physics text. If t is the age of the carbon in years,
(1/2)^(t/5568) = 0.1429
t/5568 = ln0.1429/ln(1/2)= 2.807
t = 15,630 years.
Using your equation,
C(t)/C0 = 0.1429 = e^.-0001216t
-0.0001216t = ln .1429 = -1.9456
t = 16,000 years
(1/2)^(t/5568) = 0.1429
t/5568 = ln0.1429/ln(1/2)= 2.807
t = 15,630 years.
Using your equation,
C(t)/C0 = 0.1429 = e^.-0001216t
-0.0001216t = ln .1429 = -1.9456
t = 16,000 years
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