Explanation:

It takes carbon-14 isotope sample $5,730$ years to decay to half of the amount

Let us count the decays from $16,000$ to $500$

$\frac{16,000}{2} = 8,000$

$\frac{8,000}{2} = 4,000$

$\frac{4,000}{2} = 2,000$

$\frac{2,000}{2} = 1,000$

$\frac{1,000}{2} = 500$

Since, we have $5$ decays and each decay will take $5,730$ years. Therefore, $(5)(5,730) = 28,650$ years