Given that the half-life of the sample is 14.28 days, you are looking for a decay factor [tex]k[/tex] such that
[tex]\dfrac12=e^{14.28k}[/tex]
Solving for [tex]k[/tex] yields
[tex]\dfrac12=e^{14.28k}[/tex]
[tex]\ln\dfrac12=\lne^{14.28k}[/tex]
[tex]-\ln2=14.28k[/tex]
[tex]k=-\dfrac{\ln2}{14.28}\approx-0.0485[/tex]
Now, after 57 days, you're told that a sample of unknown mass decayed to 55g, which means if [tex]M[/tex] was the starting mass of the sample, then
[tex]55=Me^{57k}[/tex]
Solving for [tex]M[/tex] yields
[tex]M=\dfrac{55}{e^{57k}}\approx874.889\text{ g}[/tex]
