Answer:
The answer is "17200 years".
Explanation:
Given:
[tex]A = 20 \ \frac{counts}{minute}\\\\A_{o} = 160\ \frac{counts}{minute}[/tex]
Let the half-life of carbon-14, is beta emitter, is [tex]T = 5730\ years[/tex]
Constant decay [tex]\ w = \frac{0.693}{ T}[/tex]
[tex]= 1.209 \times 10^{-4} \ \frac{1}{year}\\[/tex]
The artifact age [tex]t= ?[/tex]
[tex]A = A_{o} e^{-wt} \\\\e^{-wt} = \frac{A}{A_{o}}\\\\-wt = \ln \frac{A}{A_{o}}\\\\= -2.079\\\\t = 1.7199 \times 10^{4} \ years\\\\\sim \ 17200\ years\\[/tex]
