math
posted by hannah on .
1.The remains of an old campﬁre are unearthed and it is found that there is only 80% as much radioactive carbon14 in the charcoal samples from the campﬁre as there is in modern living trees. If the halflife of carbon 14 is 5730 years, how long ago did the campﬁre burn?

Po = Poe^kt
1/2 = e^5730k
Ln(1/2) = Lne^5730k
Ln(1/2) = 5730k
K = ln(1/2)/5730
Poe^ln(1/2)/5730 *t
.80P0 = Poe^ln(1/2)/5730 *t
.8 = e^ln(1/5)/5730 t
ln(.8) = ln(.5)/5730t lne
ln(.8) = ln(.5)/ 5730 t
t = 5730ln(.8)/ln(.5) 
t=1844.65 years

found in an Egyptian pyramid contains 75% of its original carbon_14 which has about 5730 years as halflife.