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