An archeologist finds an artifact that contains 44% of the carbon-14 that it would have had originally. What is the estimated age of the artifact? (The half-life of carbon-14 is 5,730 years.)

Question

mathstudent55 · Answer

Are you given a formula for calculating age using carbon-14 dating?

anonymous · Answer

no :(

anonymous · Answer

$$.44=\left(\frac{1}{2}\right)^\frac{t}{5730}$$ solve for $t$

anonymous · Answer

in two steps 
$$\frac{t}{5730}=\frac{\ln(.44)}{\ln(.5)}$$
$$t=\frac{5730\ln(.44)}{\ln(.5)}$$ and a calculator

anonymous · Answer

thank you sooo much!! so is that the final answer?

anonymous · Answer

if you want a number, use a calculator

anonymous · Answer

to fine the estimated age

anonymous · Answer

looks like about 6787 http://www.wolframalpha.com/input/?i= \frac{5730\ln%28.44%29}{\ln%28.5%29}

anonymous · Answer

of the artifact

anonymous · Answer

i got 	t=6786.75

anonymous · Answer

maybe this one will work better http://www.wolframalpha.com/input/?i=5730*ln%28.44%29%2Fln%28.5%29

anonymous · Answer

thank you so much!!!

anonymous · Answer

yw