Originally Posted by

**centenial** Hello,

I could use some help with the following question.

The half-life of $\displaystyle C^{14}$ is 5730 years. If a sample of $\displaystyle C^{14}$ has a mass of 20 micrograms at time 0, how long will it take until (a) 10 micrograms, and (b) 5 micrograms are left.

Here's what I have:

To solve, I use the exponential decay formula:

$\displaystyle N = N_0e^{kt}$

First, I solve for k:

$\displaystyle 10 = 20e^{5730k}$

$\displaystyle \frac{1}{2} = e^{5730k}$

$\displaystyle ln(\frac{1}{2}) = 5730k$

$\displaystyle -ln(2) = 5730k$

$\displaystyle \frac{-ln(2)}{5730} = k$

But, here I am stuck, because the value of $\displaystyle \frac{-ln(2)}{5730}$ is a very long non-terminating decimal. How am I supposed to use this in the exponential decay formula?

thanks