Question #d0547

1 Answer
Mar 3, 2016

Answer:

#21000 "years"#

Explanation:

For each half-life, the amount of #"C"-14# would be halved. So after #x# number of half-lives, where #x# is a positive integer, the amount of #"C"-14# left would be #1/2^x#. Turns out that this also works for #x# not being an integer (but #x# still has to be positive).

So now we want to solve

#1/2^x = 8%#

Which is

#x = log_2(1/(8%))#

#~~ 3.64#

In terms of number of years, it would be

#x * (5700 "years") = 3.64 * (5700 "years")#

#~~ 21000 "years"#