How long ago did the wooly mammoth disappear from North America?

[chawkdee]

Bones of the wooly mammoth have been found in North America. The youngest of these bones has a 14C activity per gram of carbon that is about 21% of what was present in the live animal. How long ago (in years) did this animal disappear from North America?

I'm struggling with this problem - is it simply a mathematical problem - working out how many half-lives (5730 years) cause 21% to be left?
Or, do i have top work out the Decay constant λ then use ΔN/Δt = -λ N ?

If it is simply a mathematical Can anyone tell me how to do it please.
If I have to find the Decay constant, I'm still stumped on the mathematics involved.

Thanks for any help.

Chawkdee

 

[mgb_phys]

You just need the ratio of N_now, N_orig and the half life.
The equation is derived here http://en.wikipedia.org/wiki/Half-life

Hint, estimate how many half lives you would need to get 25% of the c14 left - it's easy to get logs the wrong way around in the calculator

 

[cepheid]

Well, both methods are mathematical! There is no difference between them. The differential equation dN/dt = -λN has an exponentially decaying solution: N(t) = N₀e^-λt, where the constant N₀ is the original amount.

You can easily express this as an exponential function having base 2 instead of base e. That will tell you the relation between the half-life and λ. That is how the two methods are related. That having been said, since you already know the half-life, you can probably use the first method you suggested.

 

[chawkdee]

Thanks a lot - great help!