Question 1192688
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..