Question

Situation:

Answer 1

Answer:

t = 6162  years

Step-by-step explanation:

Apparently you are asked to use the constant k = 0.0001 instead of the most common 0.00012. We'll answer the problem using such number you typed, but make sure that there is no omission in your typing.

The equation to use is that for carbon decay:

$N(t)=N_0\,e^{-0.0001\,\,t}$

If the skull contains 54% of its original amount of C14, then that means that :

$N(t)=0.54 \,\,N_0$

we use this to solve for the time (t) in our equation:

$0.54\,\,N_0=N_0\,e^{-0.0001\,\,t}\\\frac{0.54\,\,N_0}{N_0}=e^{-0.0001\,\,t}\\0.54=e^{-0.0001\,\,t}\\ln(0.54)=-0.0001\,\,t\\t=\frac{ln(0.54)}{-0.0001} \\t=6161.86\,\,years$

which rounded to the nearest year as requested gives :

t = 6162  years