Question

A wooden boat is discovered just south of the Graet Pyramid in Egypt had a Carbon-14 content of approximately 25% of that found in living organisms. How old is the boat? (The half-life of Carbon-14 is 5,715 years.)

Answer 1

Because 25% is half of 0.5 and the half life of
`{}^(14)\text{C}` is given as 5,715, the time it takes to reach this amount should just be double the half life: 11430 years.

However, in other cases the problem may not have easy numbers, so below is a more mathematical approach.

The half life formula is
`A=A_0*((1)/(2) )^{(t)/(h) }`.

Solving for t gives:

`t=(h*\ln((A)/(A_0) ))/(\ln((1)/(2) ))`

Given information:

`A=0.25A_0\\h=5715\text{ yrs}`

Plug in given values and solve for t.

`t=(5715 *\ln(0.25) )/(\ln((1)/(2) )) =11430 \text{ yrs}`

With correct significant figures, this would be 11000 years.