Carbon dating?

Question

The half-life of Carbon-14 is 5730 years.

The equation expressing radioactive decay is
N=(No)e-kt (-kt is raised)

N=amount at time t
No=amount of substance at time 0
e=2.718(roughly)
k=constant

How old is an animal bone that has lost 30% of it`s carbon-14?

I`m not sure if you rely solely on the above equation.

Answer 1

You can first look at this intuitively and then use your formula.

Carbon 14 content will decrease by 50% in 5730 years. So if your sample has lost 30% of the C-14, it should be approx. 60% of the 5730 year half life, or approx. 3500 years old.

Now use your formula to see what exact answer you get, keeping in mind it should be close to the estimated approximation.

Answer 2

If half life is known, you better use
N=(No) x 2^(-t/T) with T = half life
N/(No) = 2^(-t/T)
30% = 2^(-t/T) = 0.30
(-t/T) x log(2) = log(0.30) both base 10
t/T = -log(0.30)/log(2)
t / (5730 years) = 1,736965594
t = 5730 years x 1,736965594 = 9952,812854 years
t = 10 x thousand years = 10 ky

Th