How old is a bone if it still has 50% of its carbon-14 content?

5730 years

Explanation:

The half life of carbon-14 is 5730 years. If 50% of the carbon-14 remains, then exactly 1 half life has passed.

The half-life equation is:

A = A₀ (½) ^ (t / T)

where A is the remaining amount,

A₀ is the initial amount,

t is time,

and T is the half life.

In this case, A = ½ A₀ and T = 5730.

½ A₀ = A₀ (½) ^ (t / 5730)

½ = (½) ^ (t / 5730)

1 = t / 5730

t = 5730