Since they lost 69.1 %, only 30.9 % remains. The correct equation for the remaining amount is
[tex]A(t)=A_0(0.5)^{\frac{t}{5750}}[/tex]
t = years since 100% was present, A0 = initial amount = 100% .
Get time T to drop to 30.9% from
[tex]30.9=100(0.5)^{\frac{T}{5750}}[/tex][tex]0.309=(0.5)^{\frac{T}{5750}}[/tex]
Take log both sides,
[tex]\log 0.309=\frac{T}{5750}\log 0.5[/tex][tex]-0.51004=\frac{T}{5750}(-0.30103)[/tex][tex]1.694=\frac{T}{5750}[/tex][tex]T=9742.3\text{ years}[/tex]
Hence the bones are 9742.3 years old when they are discovered.
