The carbon14 decay rate of a sample obtained from a young tr

The carbon-14 decay rate of a sample obtained from a young tree is 0.226 disintegration per second per gram of the sample. Another wood sample prepared from an object recovered at an archaeological excavation gives a decay rate of 0.110 disintegration per second per gram of the sample. What is the age of the object?

I am putting -ln (.11/.226)*5730 =4125.91... however 3 significant =\\ inputting 4130 and its still wrong...

Solution

0.110 / 0.226 = 0.4867, which is a little less than 1/2 (as in a little less than 1 half-life). But, you just can\'t take the artithmetic ratio of 0.5 / 0.4654, because the decay is exponential, not linear.

The real ratio would be given by the formula:

disintegration rate of old thing = 0.226 * e^(-time/5730)

5730 years is the half-life of C-14

time is in years

0.226 is the initial rate

So plug in 0.110 and solve for time.

0.110 = 0.226 * e^-(time/5730)

0.4867257 = e^-(time/5730)

ln(0.4867257) = -time/5730

I think you can get it from there.