SOLUTION: Help with this log problem. I have the answer but am confused on how to get to it Prehistoric cave paintings were discovered in a cave in France. The paint contained 39% of the

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Help with this log problem. I have the answer but am confused on how to get to it Prehistoric cave paintings were discovered in a cave in France. The paint contained 39% of the       Log On


   

Question 898557: Help with this log problem. I have the answer but am confused on how to get to it
Prehistoric cave paintings were discovered in a cave in France. The paint contained 39% of the original carbon-14. Use the exponential decay model for carbon-14, A = Ao e ^(-0.001211)(t) to estimate the age of the paintings.
The paitings are approximately 7.782 years old.
Can someone please show me how to arrive at that answer?
thank you
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Your decay equation is A=Ao*e^(-0.001211t) in pure text and using your same variables. This will appear more conventionally as A=Ao%2Ae%5E%28-0.001211t%29.

You are given a relationship between A and Ao, and are asked for t. Solve first symbolically for t, which is a more comfortable process.

ln%28A%29=ln%28Ao%29%2Bln%28e%5E%28-0.001211t%29%29
ln%28A%29=ln%28Ao%29%2B%28-0.001211t%29%2A1
ln%28A%29-ln%28Ao%29=-0.001211t
ln%28Ao%29-ln%28A%29=0.001211t
highlight_green%28t=%281%2F0.001211%29ln%28Ao%2FA%29%29

You were given A is a percentage of Ao, so take Ao as 100 and A as 39.
Now just substitute into the formula for t:
t=%281%2F0.001211%29ln%28100%2F39%29
...with a calculator for help....
highlight%28t=778%29 years.


This showed at four significant figures to be 777.5 years, but how accurately you can trust the decay equation can be debated. You most likely made a decimal mistake in your steps.