Answer:
10,000 years
Explanation:
Given that,
Half life of the radioactive isotope, [tex]t_{\frac{1}{2}}[/tex] = 5000 years
Initial composition, [tex]N_0[/tex] = 16 grams
Final composition, [tex]N[/tex] = 4 grams
We know that,
[tex]N=N_0\times (\dfrac{1}{2})^\frac{t}{t_\frac{1}{2}}}\\\\4=16(0.5)^\frac{t}{5000}}\\\\\dfrac{4}{16}=(0.5)^{\frac{t}{5000}}\\\\0.25=(0.5)^\frac{t}{5000}\\\\0.5^2=(0.5)^\frac{t}{5000}\\\\2=\dfrac{t}{5000}\\\\t=2\times 5000\\\\t=10000\ yrs[/tex]
Therefore, the age of the rock is 10,000 years.
