an archaeologist in Turkey discovers a spear head that contains 53% of its original amount of c-14. find the age of the spear to the nearest year

Question

ganeshie8 · Answer

okay to estimate the age of spear head you need to know half life of c-14. you know it ?

anonymous · Answer

um i dnt know any of this i know that k=0.0001

ganeshie8 · Answer

k is rate of decay ?

ganeshie8 · Answer

if k is rate of decay we can put below equation :

$53 \% = e^{-kt} $

plug in k and solve for t

anonymous · Answer

yea i never learned this in school im tryin to help a friend and i dnt know how to fnd any of it

ganeshie8 · Answer

np :)

they are easy if you are familiar with exponential functions. but you will be fine by just using the formula and find the unknown variable for now... 

use below formula of radioactive decay :

$\huge  \% \ left = e^{-kt}$

k : rate of decay
t : time in years

anonymous · Answer

i knw people said that e is 2.718

ganeshie8 · Answer

here, 

$53 \% = e^{-.0001 * t}$

$.53 = e^{-.0001 * t}$

$.53 = \frac{1}{e^{.0001 * t}}$

$ e^{.0001 * t} = \frac{1}{.53} $

$.0001*t = \ln (1/.53)$

$t = \ln(1/.53)/.0001$

t = 6348.78 years

ganeshie8 · Answer

what this means is : that spearhead took ~ 6349 years to shrink to 53 %...

anonymous · Answer

thankyou soo much you r the only one to put it all there for me to understand

ganeshie8 · Answer

np you're welcome :DD

anonymous · Answer

6349