In the year 2005, a picture supposedly painted by a famous artist some time after 1815 but before 1865

Question

contains 98.4 percent of its carbon-14 (half-life 5730 years).

(a) From this information, could this picture have been painted by this artist?
(b) Approximately how old is the painting

Answer 1

you know that the fraction of C₁₄ after t years is
(1/2)^(t/5730)

So, now you just need to find t such that
(1/2)^(t/5730) = 0.984
and check to see whether that number of years fits the time period specified.