Carbon 14 has a half-life of 5730 years. That means that if the initial amount of C14 is a.?

Question

Determine the amount of A(T) of C14 in an organism 5730,11460, 1000, 15000, 17190, years after it died., if the amount of C14 present while the organism was living is 100g. (Hint: notice that 1000 = (1000 / 5730) * 5730

Answer 1

Don't know how good you are in powers of 2, but here goes:

The concept of half-life is that in each interval, the amount of isotope will decrease to 50% of its initial amount at the start of the interval. This is independent of the initial mass. In higher math, we call this a first order decay, but I doubt if you are into that math. So after 5730 years after death, we have one-half life loss, or that the mass of C-14 is now 50g

For t=11460 years, we have two one-half life losses, or the mass of C-14 is now 25 g (1/4th the original

For t= 1000 years, we have about 0.17 half lives. So the amount remaining will be 100 x 1/(2^0.17).

For t= 15000 years, we have about 2-5/8 half lives. (15000/5730) So the amount remaining will be 100 x 1/(2^2.62) appx.

Last part, we have 3 half-lives, so only 1/8 initial amount remains, or 12.5 grams.