Question

A geologist in South America discovers a bird skeleton that contains 80% of its original amount of C-14. N0= initial amont of C-14 (at time t=0) N= amount of C-14 at time t t= time, in years k= 0.0001 Find the age of the bird skeleton to the nearest year

Answer 1

A geologist in South America discovers a bird skeleton that contains 80% of its original amount of C-14

We use formula $N = N_oe^{-kt}$

N0= initial amont of C-14 (at time t=0)

N= amount of C-14 at time t

t= time, in years

k= 0.0001

N is 80% of N0 that is $N= 0.80N_o$

$N = N_oe^{-kt}$

$0.80N_o = N_oe^{-kt}$

Divide both sides by N_o

$0.8=e^{-0.0001 t}$

Take ln on both sides

$ln(0.8)=lne^{-0.0001 t}$

ln(0.8) = -0.0001t ln(e)

ln(0.8) = -0.0001t

Divide both sides by -0.001

t = 2231.435513

The age of the bird skeleton is 2231 years old