Posted by **Hanna** on Tuesday, October 11, 2011 at 7:58pm.

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.

- 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 "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)

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