$(2$ points$)$ In the year $2005,$ a picture supposedly painted by a famous artist some time after $1875$ but before $1925$ contains $96\mathrm{.}6$ percent of its carbon$-14($half$-$life $5730$ years$).$

From this information, could this picture have been painted by this artist? $$

Approximately how old is the painting? $$ years

$(2$ points$)$ In the year $2005,$ a picture supposedly painted by a famous artist some time after $1875$ but before $1925$ contains $96\mathrm{.}6$ percent of its carbon$-14($half$-$life $5730$ years$).$

From this information, could this picture have been painted by this artist? $$

Approximately how old is the painting? $$ years