Half life question

Question

n the year 2005, a picture supposedly painted by a famous artist some time after 1615 but before 1665 contains 98.9 percent of its carbon-14 (half-life 5730 years).
From this information, could this picture have been painted by this artist?

Answer 1

To be "authentic" the percentage of carbon-14 in the painting must be more than that for 1615 yet less than that for 1665.

 

For 1615:

 

(0.5)^390/5730

(0.5)^39/573

(0.5)^13/191

(0.5)^0.068
0.954

95.4%

 

The painting could have been painted after 1615.

 

For 1665:

 

(0.5)^340/5730

(0.5)^0.593

0.9597

96%

 

At 98.9% the painting has too much Carbon-14 to have been painted before 1665.