SOLUTION: Skeletal remains had lost 85% of the C-14 they originally contained. Determine the approximate age (in years) of the bones. (Assume the half life of carbon-14 is 5730 years. Round

Question 1192688: Skeletal remains had lost 85% of the C-14 they originally contained. Determine the approximate age (in years) of the bones. (Assume the half life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)

Found 4 solutions by Theo, greenestamps, ikleyn, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
half life of carbon is 5730 years.
formula to use is 1/2 = g ^ n
g is the growth rate.
n is the number of years.
you are given that n = 5730.
formula becomes 1/2 = g ^ 5730
take the 5730th root of both sides of the equation to get:
(1/2) ^ (1/5730) = g
solve for g to get:
g = .9998790392
that's the annual growth rate of the carbon.
since it's less than 1, the carbon is decaying by that factor.
to confirm, take 1 * .9998790392 ^ 5730 and you will get 1/2.

if the skeletal remains had lost 85% of their carbon, then only 15% remains.
using the annual growth rate you just calculated for the half life, the formula becomes:
.15 = .9998790392 ^ n
take the log of both sides of this equation to get:
log(.15) = log(.9998790392 ^ n)
since log(x^n) = n * log(x), this becomes:
log(.15) = n * log(.9998790392)
divide both sides of this equation by log(.9998790392) to get:
log(.15)/log(.9998790392) = n
solve for n to get:
n = 15682.81286.

the carbon should be reduced to 15% in 15682.81286 years.
.9998790392 ^ 15682.81286 is equal to .15.
this confirms the equation is good.

i did not use the displayed numbers to perform the calculations.
i used the numbers that were stored by the calculator into calculator memory locations.
those numbers are more accurate than the displayed numbers.
if you use the displayed numbers, you will get close to what i got but you will not be right on.
the difference, however, will be very very small..

Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!

The fraction of the original amount remaining is (1/2)^n, where n is the number of half lives. Since 85% has been lost, 15% remains. So

to 3 decimal places

The age of the remains is 2.737 half lives:

to the nearest year.

Note rounding the age to the nearest whole number is not really reasonable, because radioactive decay is a statistical process which is only APPROXIMATELY exponential.

ANSWER (according to the instructions): 15683 years

A more correct answer: ABOUT 15700 years

Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
.

If you don't care about quality of the solution, you may accept it from the Theo's post.

But if you will come to a respectful company for an interview and if they will give you a similar problem,

then, if you solve it in that way, they will fail you.

Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
; initial amount, A, final amount, y, time in years x.

Lost 85% means kept 15% as remaining

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