Question

The half-life of carbon-14, which is used in dating archaeological finds, is 5730 yr. Assume that 100% of the carbon-14 is present at time 0 yr, or x=0. Write the equation that expresses the percentage of carbon-14 remaining as a function of time.

Answer 1

Amount left = (1/2)^(x/5730)

check:
if x = 0 , amount left = (1/2)^0 = 1 = 100%

if x = 5730 , amount left = (1/2)^(1) = 1/2 = 50%

formula is good!

Answer 2

Thanks so much!
Could you tell me the base formula used for that?

Answer 3

normally I would have used \
amount = a(e^(kt)) where a is the initial amount, in your case it was 1 for 100%
and k is some constant.

but since they were talking about "half-life" I used 1/2 as the base

for half-life questions,
amount = a(1/2)^(t/half-life period)

in your case
amount = 1(1/2)^(t/5730)