Answer:
The age of the pottery bowl is 12,378.7 years
Step-by-step explanation:
The amount of C-14 after t yeas is given by the following equation:
[tex]N(t) = N(0)e^{-kt}[/tex]
In which N(0) is the initial amount and k is the decay rate.
In this question, we have that:
[tex]k = 0.0001[/tex]
So
[tex]N(t) = N(0)e^{-0.0001t}[/tex]
Age of the pottery bowl:
29% of its original amount of C-14. So we have to find t for which N(t) = 0.29N(0). So
[tex]N(t) = N(0)e^{-0.0001t}[/tex]
[tex]0.29N(0) = N(0)e^{-0.0001t}[/tex]
[tex]e^{-0.0001t} = 0.29[/tex]
[tex]\ln{e^{-0.0001t}} = \ln{0.29}[/tex]
[tex]-0.0001t = \ln{0.29}[/tex]
[tex]t = -\frac{\ln{0.29}}{0.0001}[/tex]
[tex]t = 12378.7[/tex]
The age of the pottery bowl is 12,378.7 years
