Question

An archaeologist finds a wood fragment that has 110110 of the original proportion of Carbon-14. How old is the piece of wood? The decay constant of Carbon-14 is .00012.00012. (Give an answer accurate to 2 decimal places.)

Answer 1

latest amount has to be in form of percentage. i think its 11% instead of 110

decay equation is of the form N(t)=N_oe^-kt where N_o is the original amount , t is time ,N(t) is amount after time t, k is decay constant

given the decay constant of Carbon-14 is 0.00012. so k=0.00012

=>N(t)=N_oe^-0.00012t

given wood fragment that has 11% of the original proportion of Carbon-14
=>N(t)=(11_/100)N_o
=>N_oe^-0.00012t =(11_/100)N_o
=>e^-0.00012t =(11_/100)
=>e^0.00012t =(100_/11)
=>0.00012t =ln(100_/11)
=>t =(1_/0.00012)ln(100_/11)
=>t =18393.9576.....

piece of wood is 18394 years old

if original proportion of Carbon-14 is different please comment.i will change the solution