Question

Carbon-14 has a half-life of 5700 years. In a living organism, the ratio of radioactive carbon-14 to
ordinary carbon remains fairly constant during the lifetime of the organism. After the organism’s
death no new carbon is integrated into the organism’s remains, so the proportion of carbon -14 in the
remains decreases according to the law of exponential chance. The variable of interest here is the
percent the original amount of carbon-14 present in the organism’s remains.
a) Find the exact value of k for the decay equation for carbon-14.
b) If a painting attributed to Vermeer (1632-1675) was painted 5 years before his death,
approximately what percentage of carbon-14 should it contain? Round off your answer to the nearest tenth of a percent.
c) The painting was declared a forgery because it contained 99.5% of its original carbon-14. Based
on the law of exponential decay, find the true age of the painting. Round off your answer to the nearest year.

Answer 1

A(t) = Ao * 2^(-t/5700)

If you want that to use e instead of 2, then since 2 = e^ln2,

A(t) = Ao * e^(-ln2/5700 * t)
and k = ln2/5700.

Now just plug in your numbers to answer the other questions.

Answer 2

It cannot be determined, since carbon dating is very inaccurate

Answer 3

such