## anonymous 5 years ago Situation: A geologist in South America discovers a bird skeleton that contains 80% of it's original amount of c-14. Find the age of the bird skeleton to the nearest year.

1. anonymous

you need the half life of c-14 or else the "k-value" without it you cannot solve this.

2. anonymous

k = .0001

3. anonymous

ok now we can do it. first of all no matter what you start with you will have 80% when you are done. 80% = .8 so solve $.8=e^{-.0001t}$for t $ln(.8)=-.0001t$ $t=\frac{ln(.8)}{-.0001}=2231$

4. anonymous

btw i hope it is clear why it doesn't matter what you start with. if you start with 100 grams then 80% of that is 80 so you would put $80=100e^{-.0001t}$ and the first step would be to divide by 100 to get $.8=e^{-.0001t}$

5. anonymous

then what?

6. anonymous

oh then to get the variable out of the exponent take the natural log.

7. anonymous

$e^y = x$ same as $y=ln(x)$

8. anonymous

so if $e^{-.0001t}=.8$ same as $-.0001t=ln(.8)$

9. anonymous

then divide to -.0001 to get t. done