An artifact was found and tested for its carbon-14 content. If 82% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.

Question

anonymous · Answer

The basic formula for this kind of problem is 
$$\large N = No\ e^{-kt}$$

anonymous · Answer

$$\large .82=\left(\frac{1}{2}\right)^{\frac{t}{5730}}$$ solve for $t$

anonymous · Answer

Another useful thing is that if the half-life is T
T k = ln(2)

anonymous · Answer

You want to work through that one, I think?

anonymous · Answer

you have a choice, you can use @telliott99 method, find $k$ and then solve, or you can solve the equation i wrote using the change of base formula
that method gives 
$$t=5730\times \frac{\ln(.83)}{\ln(.5)}$$

anonymous · Answer

@satellite73 
sure you want that 1/2 in the base

anonymous · Answer

Is that part of your change of base, I have to work through that  ..