As we discussed in class on earth the ratio of carbon 14 to

As we discussed in class, on earth the ratio of carbon 14 to carbon 12 years after the death of an organism is given by r=1/10^12 e^(-t/8223)

On your vacation you find a beautiful ancient woven basket where the ratio of carbon 14 to carbon 12 is 0.72*10^-12. It is approximately how many years old?

Solution

R= (1/10^12)e^(-t/8223)

Here R=.72*10^-12

.72*10^-12= (1/10^12)e^(-t/8223)

.72*10^-12 *10^12= e^(-t/8223)

.72= e^(-t/8223)

Taking ln on both sides

ln .72= -t/8223

t=-8223 ln.72

t=2701 yrs approx