Answer
a) 94.13 % b) $t \approx 588$ years
Work Step by Step
a) The half life for carbon is 5730 years.
so, $k=\dfrac{\ln 2}{5730}$
$C=C_0e^{-\dfrac{\ln 2}{5730}t}$
Now, at $t=500$
$ C=C_0e^{-\dfrac{\ln 2}{5730}(500)}$
so, $C \approx 0.9413 C_0$
This means that 94.13 % of carbon-14 is present in the Ice Maiden.
b) The half life for carbon is 5730 years.
so, $k=\dfrac{\ln 2}{5730}$
$C=C_0e^{-\dfrac{\ln 2}{5730}t}$
Now, at $C=0.9313 C_0$
$0.9313 C_0=C_0e^{-\dfrac{\ln 2}{5730}(t)}$
so, $t \approx 588$ years