Question

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.

Answer 1

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

Answer 2

k = .0001

Answer 3

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
\[ln(.8)=-.0001t\]
\[t=\frac{ln(.8)}{-.0001}=2231\]

Answer 4

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
\[.8=e^{-.0001t}\]

Answer 5

then what?

Answer 6

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

Answer 7

\[e^y = x\] same as \[y=ln(x)\]

Answer 8

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

Answer 9

then divide to -.0001 to get t. done