9 Carbon Dating In 1970 Amos Flora of Flora Indi ana discove

9. Carbon Dating. In 1970, Amos Flora of Flora, Indi- ana, discovered teeth and jawbones while dredging a cree mastodon and had lost 77.2% of their carbon-14. How old were the bones at the time they were discovered? (Sources: \"Farm Yields Bones Thousands of Years Old,\" by Dan McFeely, Indianapolis Star, October 20, 2008; Field Museum of Chicago, Bill Turnbull, anthropologist)

Solution

For Radioactive decay,

N(t)=No(t) e^-vt

where t is time in years, v is decay constant , N(t) concentration remaining , No(t) is the inital concentration

carbon-14 lost = 77.2%

carbon -14 remaining = N(t) = No(t)(100% - 77.2%) = 22.8%No(t)

v for carbon dating = 0.00012096

using value in the equation  N(t)=No(t) e^-vt

=> 22.8%No(t)= No(t) e^-0.00012096t

=> 22.8/100=  e^-0.00012096t

^{taking log}

^{=.> ln(0.228) = -0.00012096t}

^{=> -1.47840965= -0.00012096t}

=> t = 12222.30 years

Bones were 12222 years old