Posted by Hanna on Tuesday, October 11, 2011 at 7:58pm.
The halflife of carbon14, which is used in dating archaeological finds, is 5730 yr. Assume that 100% of the carbon14 is present at time 0 yr, or x=0. Write the equation that expresses the percentage of carbon14 remaining as a function of time.

Math  Reiny, Tuesday, October 11, 2011 at 8:08pm
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!

Math  Hanna, Tuesday, October 11, 2011 at 8:21pm
Thanks so much!
Could you tell me the base formula used for that?

Math  Reiny, Tuesday, October 11, 2011 at 9:10pm
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 "halflife" I used 1/2 as the base
for halflife questions,
amount = a(1/2)^(t/halflife period)
in your case
amount = 1(1/2)^(t/5730)
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