#### Answer

The fossil $6658.3$ years old.

#### Work Step by Step

The half life for carbon is 5700 years.
Radioactive decay formula is: $y_0e^{-kt}=0$
This implies that
$k=\dfrac{\ln 2}{5700}$
$e^{-\dfrac{\ln 2}{5700}t}=0.445$
Thus, $-\dfrac{\ln 2}{5700} t=\ln (0.445)$
so, $t=6658.3~years$