A portion of fossilized bone has lost 97% of its original amount of carbon-14,
which has a half-life of 5730 years. Assuming exponential decay, estimate the age of the fossil.
Can someone explain how to solve this?

Question

A portion of fossilized bone has lost 97% of its original amount of carbon-14,
which has a half-life of 5730 years. Assuming exponential decay, estimate the age of the fossil. 
Can someone explain how to solve this?

anonymous · Answer

(3/100)P=P(1/2)^(t/5730) I don't understand where the 3/100 came from..

anonymous · Answer

hmm that would make sense....but if I didn't know that I would of put 97/100..

anonymous · Answer

dN/dt = - k N

dN/N = - k dt

ln(N) = -k t

N(t) = N(0) exp(-k t)

(N(5730)/ N(0) = 0.5 = exp(- k 5730)

ln(0.5)= - 5730 k

k = 0.693/5730 

97% lost means 3% left

0.03 = exp(- t 0.693/5730)

t =   -(5730/0.693)  ln (0.03)

t = 28994 years

anonymous · Answer

oh nvm I get it thanksXD

anonymous · Answer

Very good.