Question

You are on an archeological dig with a research team from the local university. The team unearths some pieces of an ancient wooden boat. When a sample of the wood is analyzed for carbon-14, scientists determine that 12.5% (or1/8) of the original amount of C-14 remains. If the half-life of C-14 is 5,730 years, how old is the wood from the boat?

Answer 1

The wood from boat is 17190 years old

Step-by-step explanation:

For first order radioactive decay-

`(N)/(N_(0))=((1)/(2))^{(t)/(t_(0.5))}`

where N is remaining amount of radioactive elements after "t" time,
`N_(0)` is initial amount of radioactive element and
`t_(0.5)` is half-life of radioactive element

Here
`(N)/(N_(0))` is 0.125,
`t_(0.5)` is 5730 years

Plug-in all the values in the above equation-

`0.125=((1)/(2))^{(t)/(5730)}`

or, t = 17190

so t is 17190 years or wood from boat is 17190 years old