The half-life of carbon-14 is 5730 years. How long will it take for 7/8 of a sample of carbon-14 to decay? 11,460 years 17,190 years 22,920 years 28,650 years

The formula for exponential decay is P_1=P_0*e^-kt. If the half-life is 5730 years, then:
.5=e^-5730k
ln .5=ln e^-5730k=-5730k ln e= -5730k
k=.00012096809
0.125=e^.00012096809t
ln 0.125=ln e^.00012096809t=.00012096809t ln e=-0.00012096809t
t=17,190 years