# math calculus

In the year 2005, a picture supposedly painted by a famous artist some time after 1815 but before 1865 contains 95 percent of its carbon-14 (half-life 5730 years).

Approximately how old is the painting? In years

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1. 0.5^(x/5730) = 0.95
x = 424

The 1815 date (195 years old) would still have

0.5^(195/5730) = 97.7%

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