Question

A fossilized leaf contains 15% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14. Solve the problem.
A. 35,828
B. 15,299
C. 1311
D. 21,839

Answer 1

Any ideas?

Answer 2

im stumped

Answer 3

So for every half-life, its carbon content decreases by 50%.
That's (0.5)^x where x is the number of half-lives.
Since each half-life is over a period of 5,600 years, then we do (0.5)^(x/5600)
So for each 5600 years passed, the content of carbon decreases by 50%.

\[Carbon Percentage = 0.5^{\frac{ x }{ 5600 }}\]

Do you know how to solve for x?

Answer 4

Here's some formulas:

Answer 5

Start: 100%
5600 years: 50%
11200 years: 25%
16800 years: 12.5%

I think we now have a good idea. No need to worry about some exact manifestation of just the right solution. Do SOMETHING that makes sense and track it down!

Answer 6

We want to solve for time so:
elapsed time = half-life * log (begng amt/ending amt) / log(2)

Answer 7

elapsed time = 5600 * log (100/15) / log(2)
elapsed time = 5600 * log (6.6666666667) / log(2)
elapsed time = 5600 * .82390874095 / 0.30102999566
elapsed time = 5600 * 2.7369655942
elapsed time = 15,327

AND here's a calculator to check that answer
http://www.1728.org/halflife.htm