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 $A=A_0*(\frac{1}{2} )^{\frac{t}{h} }$.

Solving for t gives:

$t=\frac{h*\ln(\frac{A}{A_0} )}{\ln(\frac{1}{2} )}$

Given information:

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

Plug in given values and solve for t.

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

With correct significant figures, this would be 11000 years.