Question

a scientist in Asia discovered the skeleton of a Saber-Tooth Tiger that contains 54% of its original amount of C-14. Find the age of the skeleton to the nearest year. Use formula N=Noe^-kt

Answer 1

Answer is:
6162 years

Explanation:
The given equation to use is:
N=Noe^-kt
First, we will need to define the variables of the equation as follows:
No : original amount of C-14 (at t=0)
N : amount of C-14 at certain time (t)
k : a constant equals 0.0001
t : the time in years

Now, we are given that:
The skeleton contains 54% of it's original amount of C-14. This means that:
N/No = 54% = 0.54

Substitute with this given in the equation given, we will find that the only unknown is the time (t). We can now solve for t as follows:
N=Noe^-kt
This can be rewritten as:
N/No = e^-kt
Now,
N/No = e^-kt
0.54 = e^(-0.0001t)
Take ln for both sides:
ln (0.54) = -0.0001t
-0.61618 = -0.0001t
t = 6161.86 years which is approximately 6162 years

Hope this helps :)